NIST IR 7985

Towards a Classification System of 

Manufacturing Objects for the 

Evaluation of Perception Systems

Geraldine S. Cheok

Marek Franaszek

Afzal Godil

Kamel S. Saidi

Roger Eastman

Tsai Hong
NIST IR 7985

Towards a Classification System of Manufacturing 

Objects for the Evaluation of Perception Systems

Geraldine S. Cheok 

Marek Franaszek

Kamel S. Saidi

Tsai Hong 

Intelligent Systems Division

Engineering Laboratory 

Afzal Godil

Information Access Division 

Information Technology Laboratory 

Roger Eastman

Loyola University 

Baltimore, MD

February 2014 

U. S. Department of Commerce 

Penny Pritzker, Secretary

National Institute of Standards and Technology 

Patrick D. Gallagher, Under Secretary of Commerce for Standards and Technology and Director
DISCLAIMER

Certain trade names and company products are mentioned in the text or identified in an illustration in 

order to adequately specify the experimental procedure and equipment used. In no case does such an 

identification imply recommendation or endorsement by the National Institute of Standards and 

Technology, nor does it imply that the products are necessarily the best available for the purpose.
Contents

1 Introduction .......................................................................................................................................... 1

2 Literature Review.................................................................................................................................. 3

2.1 Tangelder and Veltkamp (2008).................................................................................................... 3

2.2 Princeton Shape Benchmark – Shillane et al. (2004).................................................................... 4

2.3 Iyer et al. (2005)............................................................................................................................ 5

2.4 Corney et al. (2002)....................................................................................................................... 6

2.5 Jayanti et al. (2006)....................................................................................................................... 7

2.6 Cardone et al. (2003) .................................................................................................................... 9

2.7 Bespalov et al. (2005)..................................................................................................................11

3 Object Classification for Perception Systems .....................................................................................13

4 Creation of an Object Database..........................................................................................................18

5 Computation of Metrics......................................................................................................................20

6 Classifications......................................................................................................................................24

6.1 Manual Classification..................................................................................................................24

6.1.1 Geometric Approach...........................................................................................................24

6.1.2 Laser-based Technology Approach.....................................................................................27

6.1.3 Vision-based Technology Approach....................................................................................36

6.2 Classification based on Clustering ..............................................................................................40

7 Discussion and Summary ....................................................................................................................48

7.1 Discussion ....................................................................................................................................48

7.2 Summary and Future Work.........................................................................................................50

References ..................................................................................................................................................52

Appendix A: Objects Used in Classification Systems..................................................................................54

Appendix B: Calculated Metrics for Objects in Appendix A.......................................................................60

Appendix C: Extended List of Metrics........................................................................................................69
1 

1 Introduction

The objective of the Robot Perception for Identifying and Locating Parts for Assembly Project is to 

develop test methods to evaluate perception systems used for identifying and locating unfixtured 

manufacturing parts under static conditions. System evaluation often involves testing the system under 

various conditions to determine the influence of different factors on system performance. The 

dimensionality of the problem is very large, including the nature of the perception system, the 

manufacturing application, the environmental conditions, the requirements for identification and location 

accuracy, and the nature of the parts. Therefore, robust test methods need to be developed that would 

enable evaluation for as wide a range of factors and perception systems as possible. 

The evaluation of perception systems requires the use of parts or objects. However, manufacturing parts 

cover a wide array of parts from small parts (e.g., nuts) to large parts (e.g., airplane wings), from parts 

made of plastic to parts made of titanium, from parts that are flexible to parts that are rigid, and from parts 

that are simple (e.g., simple geometric shapes such as spheres or boxes) to parts that are very complex in 

shape (e.g., engine blocks). Thus, the selection of representative objects is a crucial task.

A solution to this task was to develop a part/object classification system. An object classification system 

will allow for the evaluation of perception systems based on objects in a particular class, and this may 

eventually lead to the development of standard reference artifacts of objects in the various classes.

A classification system will allow vendors to accurately specify the advantages and limitations of their

systems for the different classes of objects. Such a system will also allow users to determine if a 

particular system would work for their specific application/object prior to making a large capital 

investment in the equipment, to compare various perception systems, and to have confidence in the 

perception system. 

Manufacturing parts are naturally classified by application, material, fabrication method, function, 

manufacturer, and other characteristics. This study looks at commonalities in shape across natural 

categories, so the classification criteria may group flat parts whatever the function or fabrication method. 

This study focused on object shape as could be described in a computer-aided design (CAD) file, rather 

than taking into account surface finish for multiple reasons. Parts found under the hood of an automobile 

are typically kept in natural finish since their appearance is not critical. For identification, color is an 

obvious and powerful cue and can be easily considered after shape. The same is true of labels or heavily 

marked texture; and shape is key for localization and pose determination whatever the surface finish.

For the purpose of evaluating perception systems, parts can be classified by the strength of their features 

likely to be useful for perception, or more generally by a grading from easy to difficult to perceive. This 

study uses both approaches. A classification system that encompasses all manufacturing parts would be 

beyond the scope of this project. To keep within the project and program objectives, the scope for the 

classification system was narrowed down to automotive parts. Publically available CAD models were 

used to classify shapes manually and by numerical algorithms. A number of shape metrics were 

considered for classification, and a subset selected for implementation and testing.
2 

This report documents the efforts involved in trying to develop an object classification system for 

evaluating perception systems. As part of the development of an object classification system, this study 

reviewed previous publications that classify parts from the shape retrieval literature. This limited review 

is presented in Section 2 of this report. Section 3 describes some concepts that were explored or 

discussed when developing a classification system. Also presented in Section 3 are the metrics that can 

be used to characterize an object. The selection of the objects used in the classification system is 

presented in Section 4. Descriptions of the metrics used in this report and the how they were computed 

are given in Section 5. Section 6 presents the three approaches for manual classifications and an

algorithmic-based approach for classification. Section 7 presents findings from the classifications and a 

summary.
3 

2 Literature Review

A literature review was conducted to determine existing object classification systems. The goals of many 

of the classification systems are for object retrieval from a database and for manufacturing 

systems/processes (McCarthy, 1995) (e.g., Group Technology). Classifications can be based on the part 

appearance and/or shape, manufacturing process to create the part, or the function of the part. There has 

been much research on this topic especially in the field of computer vision and pattern recognition. In the 

past decade, there has been an increase in interest in object retrieval in the mechanical engineering 

domain in part due to the widespread use of CAD and the large number of CAD models available. 

However, there is limited work on three-dimensional (3D) shape searching for engineering and CAD 

applications. The remainder of this section will summarize research and/or concepts that are relevant to 

3D shape searching for engineering and CAD applications. Of particular interest are the metrics and 

methods discussed in these studies.

2.1 Tangelder and Veltkamp (2008) 

Tangelder and Veltkamp (2008) conducted a survey of 3D shape retrieval methods. In the paper, shape 

matching methods are divided into: feature based methods, graph based methods, and geometry based 

methods. 

Feature based methods depend on measuring and comparing features and are based on pure geometry of 

the shape. These methods can be sub-divided into:

1. Global features: global features characterize the global shape of the 3D model. Examples of 

these features are volume of the model, volume-to-surface ratio, area, the Fourier transform of the 

volume, or the boundary of the shape. A disadvantage of this method is that it does not 

discriminate object details well.

2. Global feature distribution: Instead of comparing global features, this method compares 

distributions of global features. Shape distributions are compared based on properties such as 

distance, angle, area, volume between random points, and shape histograms using the principal 

axes of inertia of the model (e.g., moment of inertia about the axis, average distance from the 

surface to the axis, variance of distance from the surface). 

3. “Spatial maps are representations that capture the spatial location of an object. The map entries 

correspond to physical locations or sections of the object, and are arranged in a manner that 

preserves the relative positions of the features in an object. Spatial maps are in general not 

invariant to rotations, except for specially designed maps.” (Tangelder and Veltkamp, 2008). 

4. Local features: This method accounts for surface shape in the neighborhood of points on the 

boundary of the shape. Metrics for similarity are obtained from mapping of the surface curvature 

of the object onto a unit sphere, using histograms of shape indices calculated over the entire 

mesh, and applying semi-local descriptions of object shape centered at points on the surface of 

the object (3D shape context). 
4 

Graph based methods “attempt to extract a geometric meaning from a 3D shape using a graph showing 

how shape components are linked together. Graph based methods can be divided into three broad 

categories according to the type of graph used:” 

1. Model graphs: Model graph based similarity methods are applicable to 3D CAD solid models 

and are difficult to apply to natural shapes like humans and animals. The most common “solid 

model representation methods are boundary representation (B-rep) and constructive solid 

geometry (CSG).”

2. Reeb graphs: A Reeb graph is defined as “the quotient space of a shape S and a quotient function 

f. Reeb graphs defined by a geodesic distance are suited for matching articulated objects, but they 

are sensitive to topological changes. Also, they cannot be applied to arbitrary meshes, because 

topological problems like missing faces disturb the computation of geodesic distances.”

3. Skeletons: This method uses a skeletal graph that has geometric and topological information. 

Some researchers have combined global features and skeletal graphs.

“For graph based descriptors the complexity of the exact computation of a metric obeying the triangle 

inequality prevents practical application.”

Geometry based methods can be categorized into:

1. View based similarity: The premise of this method is that two 3D models are similar if they are 

similar from all viewing angles.

2. Volumetric error based similarity: This approach is based on “calculating a volumetric error 

between one object and a sequence of offset hulls of the other object.” 

3. Weighted point set based similarity: This method is based “on shape descriptors consisting of 

weighted 3D points.” Researchers have used weights that are based on the volume of the 

component, curvature, or sum of squared distances for models aligned in the same coordinate 

frame.

4. Deformation based similarity: This method “compare[s] a pair of 2D shapes by measuring the 

amount of deformation required to register the shapes exactly.” Tangelder and Veltkamp 

commented that it would be difficult to implement this method of 3D shape matching.

2.2 Princeton Shape Benchmark – Shillane et al. (2004) 

The Princeton Shape Benchmark (PSB) (Shilane et al., 2004) contains a database of 3D models and 

software tools to compare 3D shape matching algorithms. In the paper, a review of several 3D model 

databases was conducted and some observations of these databases were made:

• Most previous databases contain a small number of classified models. 

• Most databases contain a limited range of objects. For example, some only contain household 

objects or only vehicles.

• The databases have a wide range of granularities in the classifications. For example 

“Kitchenware” and “motorcycles with 3 wheels.”

• Many classifications mix function and form. For example, “buildings” and “machine.” 
5 

The PSB classification is based mainly on semantic and functional concepts (e.g., furniture and table) and 

secondly on shape (e.g., round tables). Other potential classifications include: grouping models based on 

function, grouping based on how they are manufactured (e.g., man-made vs. natural), grouped based on 

where they are used (e.g., office vs. home vs. outdoors), and grouping based on who uses them (e.g., 

adults vs. children). The PSB allows multiple classifications – an ASCII file contains a hierarchy of class 

names; each with a different granularity. For example, three classifications in increasing coarseness 

would be tables, furniture, man-made. Additionally, the benchmark attaches several geometric attributes 

to each model such as:

• Center of mass – the average (x, y, z) coordinates of all points on the surfaces of the polygons 

• Scale – the average distance from all points on the surface of the polygons to the center of mass

• Principal axes – “eigenvectors (and associated eigenvalues) of the covariance matrix obtained by 

integrating the quadratic polynomials xi ⋅ xj with xi ∈ {x, y, z}, over all points on the surfaces 

of all polygons.” 

Of the 12 benchmarks used to compare shape matching algorithms, those of interest are:

• “D2 Shape Distribution (D2): a histogram of distances between pairs of points on the surface 

[Osada, 2001].

• Extended Gaussian Image (EGI): a spherical function giving the distribution of surface normals

[Horn, 1984].

• Shape Histogram (SHELLS): a histogram of distances from the center of mass to points on the 

surface [Ankerst et al., 1999].

• Shape Histogram (SECTORS): a spherical function giving the distribution of model area as a 

function of spherical angle [Ankerst et al., 1999].

• Shape Histogram (SECSHEL): a collection of spherical functions that give the distribution of 

model area as a function of radius and spherical angle [Ankerst et al., 1999].

• Voxel: a binary rasterization of the model boundary into a voxel grid. 

• Spherical Extent Function (EXT): a spherical function giving the maximal distance from the 

center of mass as a function of spherical angle [Saupe and Vranic, 2001].

• Radialized Spherical Extent Function (REXT): a collection of spherical functions giving the 

maximal distance from center of mass as a function of spherical angle and radius [Vranic, 2003].

• Gaussian Euclidean Distance Transform (GEDT): a 3D function whose value at each point is 

given by composition of a Gaussian with the Euclidean Distance Transform of the surface 

[Kazhdan et al., 2003].

• Spherical Harmonic Descriptor (SHD): a rotation invariant representation of the GEDT obtained 

by computing the restriction of the function to concentric spheres and storing the norm of each 

(harmonic) frequency [Kazhdan et al., 2003].” 

2.3 Iyer et al. (2005) 

In Iyer’s et al. (2005) review of 3D shape searching, shape is defined as “all the geometrical information 

that remains when location, scale, and rotational effects (Euclidean transformations) are filtered out from 

an object.” Shape searching involves the determination of similarities among 3D shapes. Included in the 

paper are discussions of: 
6 

• global feature-based techniques (e.g., moments, invariants, Fourier descriptors, and geometry 

ratios)

• manufacturing feature recognition-based techniques for CAD models

• graph-based techniques (e.g., B-Rep graph, Spectral graph, Reeb graph, skeletal graph) 

• Histogram-based techniques - sample points on the surface of the 3D model and extracted

characteristics from the sampled points.

o Shape histogram 

 Shell model – “The space is decomposed into concentric shells around the center point. 

This representation is independent of rotation.” 

 Sector model – “The space is decomposed into sectors that emerge from the center point 

of the model.” 

 Spiderweb model – a combination of the Shell and Sector models. 

o “Shape distribution represent the shape signature as a probability distribution sampled from a 

shape function measuring the geometric properties of a 3D model” 

 A3: Measures the angles between lines joining three random points on the surface of a 

3D model. 

 D1: Measures the distance between a fixed point and a random point on the surface.

 D2: Measures the distance between two random points on the surface.

 D3: Measures the square root of the area of the triangle formed by three random points on 

the surface.

 D4: Measures the cube root of the volume of the tetrahedron formed by four random 

points on the surface.

• Product information-based techniques – designed specifically for engineering parts. “Part designs 

are described either based on their manufacturing attributes or on their geometry.”

o Group technology (GT) – “coding and classification schemes attempt to capture design and 

manufacturing attributes such as the main shape and size features of the product, production 

quality, and material.” 

o Section image-based – uses 2D silhouette of parts or sections for similarity comparison. 

• 3D object recognition-based techniques 

o Aspect graph – consists of a multiple 2D views of a 3D model of the object as seen from 

various regions on a sphere encompassing the object. 

o Extended Gaussian images (EGI)

o Geometric hashing – a 3D object is broken down into basic geometric features such as 

surface points. A set of basis points are chosen and the coordinates of all other points are 

determined based on the basis points and are stored in histograms. This process is repeated 

for other basis sets.

2.4 Corney et al. (2002) 

Corney et al. (2002) proposed three convex-hull based indices as coarse filters in preliminary steps in the 

shape matching of 3D engineering data which supports the internet-based search engine ShapeShifter. 

Factors in selecting these indices include: 

• the ability of the search engine to identify similar shapes independent of size
7 

• filters that resulted in an almost complete set of correct candidates (i.e., filters did not eliminate 

correct candidates)

• Shapeshifter employs several metrics based on the model’s convex hull

Other metrics calculated in ShapeShifter include volume, surface area, aspect ratios (of an axis-aligned 

bounding box), crinkliness, compactness, number of facets, number of holes, and convex hull. Corney et 

al. used four dimensionless ratios based on the hull as filters to assess their sensitivity to object variations 

(scaling, taper, twist, feature removal, and fits in a 100 x 100 x 100 box): 

• Bounding box aspect ratio: ratio of the longest edge to the shortest edge 

• Hull crumpliness: ratio of the object’s surface area to the surface area of its convex hull

• Hull packing: proportion of the convex hull volume not occupied by the original object 

computed as �1 − Vmodel

Vhull

�

• Hull compactness: ratio of the convex hull’s surface area cubed to the volume of the convex hull 

squared

They found that: 

• the bounding box aspect ratio could potentially exclude many potential candidate matches and 

was thus excluded as a filter, 

• hull crumpliness is relatively insensitive to twisting and warps and sensitive to feature removal 

and non-uniform scaling, 

• hull packing is insensitive to all but feature removal, and

• hull compactness is relatively insensitive to tapering, is sensitive to twisting and non-uniform 

scaling, and insensitive to feature removal. 

For the three filters based on the convex hull, the optimal tolerance values were 25 % for compactness, 

50 % for packing, and 10 % for crumpliness where optimality is based on minimizing the false-negatives 

and false-positives. 

2.5 Jayanti et al. (2006) 

Jayanti et al. (2006) developed a benchmark dataset of engineering artifacts to enable evaluations of 

various shape descriptors for engineering shape retrieval. Some challenges in developing the benchmark:

• a function-based classification is difficult because parts with similar shapes have different 

functions 

• a classification based on manufacturing process is complicated by advances in manufacturing 

processes and capabilities which blurs the mapping between form and manufacturing method 

The classification of 3D models in the engineering shape benchmark (ESB) is based on shape. The ESB 

contains 867 3D CAD models in STereoLithography1

 (STL) and Wavefront Technologies’ OBJ formats, 

and is available from http://purdue.edu/shapelab. The models are initially put into three super-classes:

 

1 Also known as Standard Tessellation Library
8 

• Solids of revolution – part envelope is largely a solid of revolution

• Rectangular-cubic prism or prismatic - part envelope is largely a rectangular or cubic prism

• Thin-walled – parts with thin-walled sections and shell-like components 

These super-classes were then further divided into groups of similar shapes. For example, clusters under 

solids of revolution included bolt-like parts, container-like parts, cylindrical parts, and discs. The authors 

used the following shape representations for their benchmarking:

• Feature vector-based methods 

o Moment invariants (MI)

o Principal moments (PM)

o 3D spherical harmonics (SH)

o Surface and area based attributes 

 Surface area and volume (SAV)

 Surface area to volume ratio (SVR)

 Crinkliness and compactness (CC)

o Geometric ratios (GR) – aspect ratios of the bounding box 

• 3D shape distribution (3DSD) using the D2 shape measure

• Convex hull histogram (CHH)

• 3D shape histogram – solid angle (SAH)

• View-based representations

o Light field descriptors (LFD)

o 2.5D spherical harmonics (2.5DSH) 

o 2D shape distributions (2DSD)

The reader is referred to the paper for detailed descriptions of these shape representations. 

Precision-recall curves were used to evaluate these shape representations. “Precision is the ratio of the 

relevant models retrieved to the retrieval size. Recall is the fraction of the relevant models retrieved for a 

given retrieval size.” Some conclusions based on the results using the ESB are that the three methods 

based on 2D views (LFD, 2.5DSH, and 2DSD) consistently outperformed the other methods, with the 

LFD resulting in significantly better precision compared to all other methods. However, view-based 

methods require more computation as compared to 3D shape measures. 3D spherical harmonics (SH) 

perform reasonably well for the prismatic parts and solids of revolutions as compared to other shape 

representations. In terms of the three super-classes: 

• Thin-walled components 

o View-based methods performed better than other methods 

o 3D shape distributions, surface area, and volume performed better than more complex feature 

vectors – SH, CHH, and SAH

o SAH performs better for this class than other point-based methods 

o Of the view-based methods (LFD, 2.5DSH, and 2DSD), all three methods performed 

comparably 

• Prismatic parts

o LFD had significantly high precision for all recall levels
9 

o 2.5DSH, 2DSD, SH, and SAH consistently performed better than the 3DSD method 

o Topology-based methods did not perform well especially at lower recall values

• Solids of revolution 

o All view-based methods (LFD, 2.5DSH, 2DSD) performed significantly better than the other 

methods 

o 3DSH and CHH performed better than 3DSD 

2.6 Cardone et al. (2003) 

Cardone et al. (2003) conducted a survey of shape similarity assessment algorithms for product design 

and manufacturing applications. 3D similarity assessment is described as the generation of shape 

signatures from the 3D models and comparing them using distance functions; the larger the value, the 

more dissimilar. The shape signatures should be “representation independent and completely describe the 

features of the 3D model.” Examples of shape signatures are graphs, vectors, or ordered collections of 

numeric values. The choice of signatures is dependent on the reason for the similarity analysis. Shape 

signatures and distance functions should have the following properties: 

• Positivity – distance between two CAD models should be non-negative

• Identity (Self-similarity) – if the distance between two CAD models is zero, then the models are 

the same

• Symmetry – given solid models x and y with shape signatures S(x) and S(y), respectively, a 

symmetric distance function needs to satisfy: 

δ(S(x), S(y)) = δ(S(y), S(x)) 

• Triangle inequality – given solid models x, y, and z with shape signatures S(x), S(y), and S(z), 

respectively, the distance function must satisfy: 

δ( S(x), S(y) ) + δ( S(y), S(z) ) ≥ δ( S(x), S(z) )

• Invariance – a part may have many different representations; “the shape signature should be 

invariant with respect to the underlying representation.” The shape signature should also be 

invariant to any rotation or translation applied to the object. 

• Robustness and sensitivity – shape signature should change proportionately to the change in the 

object. If small changes are magnified and result in the conclusion that similar objects are 

dissimilar, then the measure is not robust. If there is a large change in the object which results in 

a small change in the shape signature, then it is not sensitive.

• Computational efficiency

The similarity assessment techniques were grouped into:

• Features: “Feature-based techniques evaluate the shape signature of an object based on the type, 

size, orientation, number, and other properties of the features and their interactions. Once the 

features are extracted and their significant characteristics are determined, the comparison is 

carried out using a suitable distance function.” Disadvantages include that the technique does not 

consider the gross shape of object and feature interactions complicate feature extraction. 

Techniques described in paper were developed for product design and manufacturing. 

• Spatial functions: “These techniques use shape signatures that are spatial functions. An example 

of a spatial function is the Gaussian map that maps the set of normals of a solid onto a unit 
10 

sphere. The problem of matching and comparing 2D spatial functions defined over unit sphere 

involves manipulating two degrees of freedom (the two angles needed to align the surface of a 

sphere). The main challenge in these techniques is to identify the characteristics to be represented 

using spatial functions and to determine an efficient matching procedure to compare two shape 

signatures.” 

o Local curvature distributions over mesh representations: the signature is the spherical 

representation of the curvature distribution of 3D surfaces of solids without holes. This 

technique is useful for applications where curvature is a primary factor. Advantages include 

that the measure is invariant to translation, rotation and scaling. Disadvantages are the 

restriction to solids without holes and that accuracy depends on the mesh size – a finer mesh 

increases accuracy but increases computational time.

o Slope diagram representations: this technique uses the slope diagram representation of a 

convex polyhedron. It is invariant to translation and rotation but computationally intensive 

and restricted to convex polyhedra. 

• Shape histograms: “These techniques are based on sampling of points on the surface of the 3D 

models. Several significant characteristics can be extracted from the set of points obtained.” The 

larger the number of points, the more accurate the representation, but the more expensive it is to 

compute. These techniques do not satisfy the conditions of identity and symmetry but are useful 

for detecting gross shape similarity, that is, useful as coarse filters.

Several shape functions were described in the paper but the most robust of these was the D2 

shape function.

o D2 shape function “computes the distance between two random points. This function is 

invariant to rotation and translation and is robust.” The distances between random points are 

calculated and normalized using the mean distance. “The shape distribution is the histogram 

that measures the frequency of occurrence of distances within a specified range of distance 

values.” The distance between the two models is usually computed using the L2 norm. 

• Section images: “These techniques use sections of the solids as shape signatures. Solids are 

sectioned at various places and the sections are then analyzed for similarity. A disadvantage is 

that the method is not invariant to scaling, translation, and rotation. It is best suited for parts that 

are rotationally symmetric.” 

• Topological graphs: “These techniques use topological graphs as shape signatures. These graphs 

usually represent the connectivity information of the boundary of the solid such as the adjacency 

between faces. The nodes and edges of the graph may carry additional information related to the 

solid model.” 

• Shape statistics: Shape comparison techniques commonly use basic geometric properties for

coarse comparison between objects. Some commonly used properties are volume, surface area, 

and convex hull volume. Disadvantages include that the measures do not yield sufficient 

information for detailed comparison, but can be used as coarse filters.

A table comparing the representative algorithms is given in the paper. 
11 

2.7 Bespalov et al. (2005) 

Bespalov et al. (2005) used several benchmark datasets to evaluate nine techniques for matching CAD 

data. CAD models can either be solid models or shape models represented by polygonal meshes. The 

increasing use of laser scanners has made the generation of polygonal meshes a relatively easy task. The 

matching techniques evaluated were:

• Shape based

o Shape distributions (SD) (Osada et al., 2002) 

o Shape distributions with point pair classifications (SD-class) (Ip et al., 2002) 

o Reeb graph comparison (Reeb) (Hilaga et al. 2001)

o Shape distributions with weight learning (SD-Learn) (Ip et al., 2003) 

o Scale-Space comparison (Scale-Space) (Bespalov et al., 2003) 

• Solid based

o B-Rep techniques 

 Invariant topological vector (ITV) (McWherter et al., 2001) 

 Eigenspace indexing on B-Rep graphs (Eigen-BRep) (Peabody 2002) 

o Feature based

 Model dependency graph approximate matching (MDG) (Cicirello and Regli 2002) 

 Eigenspace indexing on matching feature interaction graphs (Eigen-Feat) (Peabody 2002) 

The k-nearest neighbor classification (kNN) and conventional recall and precision measures were used to 

evaluate the techniques. Recall and precision were defined as:

recall = 

Retrieved and relevant models

Relevant models

precision = 

Retrieved and relevant models

Retrieved models ,

where 

relevant models was “the number of models that fall into the same category as the query model” 

retrieved models was “the number of models returned by a query”

retrieved and relevant models was “the number of models returned and that fell into the same 

category as the query model.”

The datasets used to evaluate the techniques were:

• Synthetic datasets

o Primitive dataset: 101 cubes, 141 cylinders, 29 tori, and 29 spheres with various 

deformations. 

o Minor topological variation dataset

 cube-holes: 16 cubes with different numbers of holes (1 to 4) – some with holes of 

different radii and some with holes of the same radius 
12 

 brick-holes: 11 rectangular box models with 0 to 4 holes of the same size in different 

locations. 

• Actual artifact dataset: 

o CAD models from the National Design Repository Dataset 

(http://edge.cs.drexel.edu/repository/) were used. 

 Manufacturing classification: 

• prismatic machined (56 models) - machined parts are typically high precision 

parts made in small batches 

• cast-then-machined (54 models) - cast-then machined parts are typically larger 

production jobs with less stringent tolerance requirements

 Functional classification: 70 models total, example functional classes: nuts, gears, 

screws, springs, linkage arms.

o LEGO Dataset – 47 components grouped by appearance: plates, wheels and gears, 

cylindrical parts, and X-shaped axles.

o Variable fidelity dataset – 40 CAD models were used to generate 40 polygonal meshes each 

of low, normal, and high fidelity (highest number of polygons), i.e., 120 models total. 

Some findings and observations from the evaluation: 

• The graph and solid based ITV and Eigen-BRep techniques performed best on the cube-holes and 

brick-holes datasets. Among the shape based techniques, the Reeb graph technique performed 

best.

• Boundary representations (B-Reps) are more useful than mesh-based representations and 

improving ways to better use B-Reps for matching would be beneficial 

• Based on the precision-recall plots, the manufacturing and functional classifications yielded 

unacceptable and “mediocre” results, respectively, for all the techniques.
13 

3 Object Classification for Perception Systems

As stated in the introduction, our purpose for developing an object classification is to evaluate perception 

systems, agnostic to the nature and details of the system. This is different from the purpose of the 

classification systems developed by most researchers in Section 2, where the intent typically was to 

develop a perception system or to evaluate specific algorithms. The purpose for the system developed by 

Jayanti et al. (2006) is closest to our purpose, with an analysis that relates general classes of objects to the 

effectiveness of particular algorithms. 

Ideally, our proposed classification system would put objects into classes where the objects in a class 

would yield similar results, good or bad, from the performance of a wide selection of perception systems. 

A particular class of objects might be easy to perceive (e.g., textured boxes), or difficult (highly curved, 

specular parts). Ideally this would be sensor agnostic, so an easy to perceive class of objects remains easy 

to perceive across all perception systems, but in practice there will remain dependences on the nature of 

the sensor and perception algorithm. A passive sensor attuned to color will work well in distinguishing 

identically shaped but differently colored objects, while a monochrome active sensor attuned to shape 

may do better with color-less but differently shaped objects. The classification system would then be 

useful in specifying which class of object is most easily perceived by which type of sensor system.

Several concepts for developing a classification system were considered. These included classification

systems based on: 

1. Technology of the perception system, such as these examples: 

a. Laser line scanner

b. Machine vision (with one or more cameras)

c. Structured light/pattern projection (may be visible or non-visible)

2. Objects with similar features or descriptors

3. A priori knowledge of issues for perception systems based on feedback from vendors, 

integrators, and users on objects that were problematic or not problematic for their perception 

systems

A logical choice would be classification based on perception system technology, giving up sensoragnostic classification in return for more effective, technology-specific categorizations. However, this 

would require acquiring intimate knowledge of the various types of perception systems and the 

availability and extensive evaluation of these systems to determine the advantages and disadvantages of 

systems that represented each of the various technologies. Given budgetary and time constraints, a 

decision was made that, as a first step, the classification system would be based on object characteristics 

and the authors’ knowledge and experience with the various technologies. 

The authors felt that a classification system that encompasses all manufacturing objects would not be 

feasible, and a narrowing of the types of objects was needed. Since the focus of the project was for bin 

picking applications, it was decided that the classification system would initially be developed for rigid, 

automotive parts found in the engine compartment and parts in the powertrain. The maximum size of the 

part/object was therefore set, arbitrarily, to be (50 x 50 x 50) cm.
14 

Given the above discussion, we compiled a set of metrics that were used by other researchers to 

characterize an object. By metrics we mean features of the object, local or global, that can be used to 

classify it. When possible, we emphasized quantitative features. The full set of metrics is given in Table 

C1 in Appendix C. Table C1 has the following information for each metric: 

• Feature: Name of feature

• Local feature: a characteristic of the object computed on a limited, local region

• Global feature: a characteristic of the object computed with global support. 

• 2D/3D/Both: Whether the feature is primarily two dimensional, three dimensional, or both. 

• Shape/Surface: Whether the feature applies primarily to the shape or surface of the object. 

• Description: Description of the metric to be computed. 

• Relevant or Non-Relevant: Whether the metric is relevant to our classification task, based 

on the judgment of the project team members. 

• Algorithm/software needed? Y/N; Available? This column indicates whether an algorithm 

or software is required to compute the metric. If an algorithm or software is needed, is it 

available?

• Source: Reference(s) in which the metric was invented or described. 

The metrics were chosen to describe a broad range of perceptual characteristics of objects, including:

• Geometry: metric properties of shape (Table 3.1) 

• Topology: relationship of components (Table 3.1)

• Viewpoint projections/appearance: features computed on 2D projections of the part (Table 

3.2) 

• Surface properties: color, texture and other (Table 3.3) 

The metrics do not provide a complete physical description of an object, as mass and material 

characteristics, aside from appearance, are not included. We were assuming that sensors would be 

primarily non-contact and utilize visual or near-infrared (IR) wavelengths and not utilize thermal IR 

bands, sonic wavelengths, magnetic, weight, or other non-visual physical properties. Also, a given shape 

described by a CAD model can be manufactured from different materials, which can result in different 

physical properties (including surface reflectance). Our primary goal was to consider those aspects of an 

object captured by shape encoded in a CAD model and that would be found in the object even if made 

with different materials. 

For the geometric metrics in Table 3.1, we selected a range of object characteristics that could be used 

either directly as a perceptual feature, or are likely to contribute to the appearance of perceptual features. 

An example would be whether the object is prismatic, with a number of flat surfaces that might lead to 

internal visual edges in an image, or rounded, with less likelihood of internal edges aside from folds and 

limbs. We were inclusive in the metrics, cataloging many with differing amounts of information rather 

than focusing on a few, high information features. The intent was not to build an efficient perception

system, but rather to understand how the metrics might partition the space of objects. 

Some geometrical metrics were selected not because they alone represented a visual feature, but because 

they may indicate the presence of visual features. In a manufacturing application, the problem of object 
15 

identification may require relatively simple discriminations, such as between a long thin object and a 

more compact one, so simple extents would be adequate. Similarly, object density (here not density of 

mass, but of shape as represented by the ratio between the volume of the object and the volume of its

convex hull) could be a marker for relatively hollow objects, like springs, that are likely to have selfocclusions.

Table 3.1. List of Selected Metrics for Object Classification.

Metric Metric Measured Comments

1 Size X,Y, Z extents

2 Size Surface area

3 Size Volume

4 Size Convex hull

5 Compactness Volume/Surface Area

6 Compactness Max/Min extent

7 Compactness (Area of Convex Hull)3/(Volume of Convex Hull)2

8 Density 1-Volume/(Volume of convex hull)

9 Flatness Short/Middle extent

10 Flatness Middle/Long extent

11 Prismatic % surface flat

12 Curvature Integrated total curvature

13 Curvature % convex, concave, saddle

14 3D 

Uniqueness # significant feature points

Use SURF2 or SIFT3 to get 

this metric (Dutagaci et al., 

2012)

15 Symmetry Rotational moments

16 Symmetry # axes+type Mirror, rotational, point

17 Antisymmetry Chirality

18 Smoothness Hull crumpliness: ratio of object surface area to surface area 

of its convex hull

19 Smoothness

Crinkliness: defined as the surface area of the model divided 

by the surface area of a sphere having the same volume as 

the model.

20 Topology # holes

Another reason for selection of some metrics is the performance of current perception systems. Many bin 

picking systems perform well on symmetric objects, such as discs and cylinders. The performance may be 

related to ease of perception, or ease of grasping, but in either case symmetry is an important metric.

Reviewing the metrics in Table 3.1, the first set (1-10 in Table 3.1) was selected to classify the 

compactness and extent of the object. The x, y, z extents, surface area and volume are basic measures of 

the object size, which are not directly useful in perception unless sensor distance or field-of-view is taken 

into account. Metric 4, convex hull, is also less useful directly but is useful as an intermediate 

computation for other metrics. 

 

2 Speeded Up Robust Features

3 Scale-Invariant Feature Transform
16 

The compactness metrics (5-7 in Table 3.1), as well as the global flatness metrics (9-10), measure ratios 

that estimate whether the object is compact in all three dimensions (metrics 5-7), or in one dimension and 

is therefore flat (metrics 9-10). Compactness alone may not be significant in ease of perception, but 

indirectly may influence other features. A flat object yields fewer possible poses and may result in 

effectively a 2D shape easy to perceive by traditional machine vision approaches. 

The density metric (8 in Table 3.1) measures the open volume of an object. The logic is: if the object is 

compact and dense, the volume of the convex hull will be close to the volume of the original object and 

the ratio would be close to 1, so the density measure will be 0. If the object is very open inside, or has 

long extensions, the volume of the convex hull will be greater than the original volume, so the ratio will 

be smaller and the density measure larger. A density measure near 1 could indicate a visually hollow 

object, like a spring, which is likely to have self-occlusions and other distinct visual characteristics. 

(Some objects may be hollow, like a box or a gas tank, but look solid from the outside – in this case the 

metric may misfire, or need to be properly interpreted.)

The second set of metrics (11-13 in Table 3.1) was selected to classify surface roundness and curvature. 

These measures have long been used in object description and perception, but are hard to describe in 

single numbers for an entire object. Curvature is a local feature (e.g., for a meshed object, the curvature is 

calculated at a vertex), and an object can have a highly curved element attached to a flat section. We 

looked for measures that would help distinguish a relatively flat object, like a box, from a highly curved 

object, like a ball bearing or a section of pipe. Our measures all essentially integrate the local curvature. 

For prismatic shapes (metric 11), the measure is the percentage of the shape that is locally flat with zero 

curvature. For more curved shapes we consider metric 12, the integrated total curvature (e.g., for a 

meshed object, the curvature averaged over all vertices). This is intended to give the average curvature 

over the entire object. Finally, metric 13 is intended to measure the percentage of the object that is locally 

convex or concave. 

The third set of metrics (14 in Table 3.1) was selected to identify objects with many distinct 3D, highcurvature local features. This would distinguish homogenous objects like a sphere from heterogeneous 

objects with many local dips, angles, and extensions, like the body of a fuel pump. In this case, there are 

many different 3D feature measures that could be used, but we determined that most measures would give 

highly correlated results at the level of discrimination we need. If an object has a large number of 

distinctive corners or bumps found by one measure, another measure is likely to also find many features 

even if not the same ones. 

The fourth set of metrics (15-17 in Table 3.1) was selected to measure symmetry. Symmetry is a complex 

concept that can be difficult to quantify on a CAD model, so the metrics were difficult to choose (and 

compute). Shapes can be symmetric by rotation, by reflection, by a helix, and other mechanisms. To 

categorize a shape’s symmetry, the nature of its symmetries has to be discovered and quantified for 

imperfect symmetries. We found the symmetry characteristic difficult to quantify and to compute, and did 

not arrive at metrics we found adequate to fully and appropriately describe symmetry. Still, symmetry can 

be important in perceptual systems – symmetric objects allow matching by techniques like generalized 

cylinders, and simple circular shapes admit to fast detectors. 

The fifth set of metrics (18-19 in Table 3.1) was selected to measure surface smoothness (roughness), 

which influences the appearance of color and texture. The two metrics essentially measure the ratio of the 
17 

object’s surface area to the surface area of an idealized version of the object (convex hull or sphere), and 

if the ratio is high, the object should have folds or other high-frequency variations in its surface.

The sixth and last class of metrics (20 in Table 3.1) was selected as a marker for topology. The measure 

we selected was the genus of the surface, or the number of holes invariant to plastic distortions. A sphere 

has zero, a torus one, and so on. These are holes completely though the object. In this case, we are not 

certain that the number of holes an object has will be significant in characterizing its appearance. A 

small, hard-to-see hole drilled though the object will increase the genus just as much as a large, 

distinguishing hole. We did not select metrics related to the branching or subpart relations of an object, 

which are sometimes described as topological. These can be complex and are beyond the scope of this 

study. 

The metrics in Table 3.2 were selected to determine the viewpoint-dependent features of an object. There 

should be some correlation between the viewpoint-independent shape metrics in Table 3.1 and the 

viewpoint-dependent metrics in Table 3.2, since density, curvature, and smoothness may influence the 

nature and number of local 2D features in 2D projections. However, we also wanted a direct measure of 

the number and distinctiveness of 2D features across possible viewpoints. The more distinctive 2D 

features, the more likely an object can be identified and located in 2D projective sensors (e.g., cameras).

Table 3.2. Metrics Based on Pose or Viewpoint.

Metric Metric Measured Comments

1 Poses # stable poses See Yee, Wan, Ventura 2001

2 Unique views Visually distinguishable poses

3 2D Uniqueness # significant 2D feature points

However, the metrics in Table 3.2 require considerable effort to compute. To properly do so, many views 

of the object have to be systematically produced, with the views simulating the camera or sensor of 

interest, and each view analyzed for the number of distinct feature points. Similarly, to determine the 

number of stable poses requires a physical simulation of the object. Also, the simulated 2D views will 

change if the object has texture. 

The metrics in Table 3.3 are material, color, texture, and reflectivity. These were selected for their 

obvious influence on object appearance. However, we did not emphasize these in the study for a few 

reasons. The first is that CAD models do not typically represent inherent surface properties, so shape is 

paramount. The second is that in manufacturing assembly, many parts do not have distinctive texture or 

color. They can be machined metal or texture-less plastic, used in internal assemblies where markings are 

not essential. The third is that surface textures can be arbitrary and highly varying, such as a single shape 

of a soft drink can that may be printed with many variations of logos and brand names. Finally, object 

appearance can vary over the object, face by face or section by section – should objects be classified on 

average appearance, maximum texture, a histogram of color or texture metrics, or some other way? 

Classifying appearance and textures for ease of perception would be another complete study. Finally, 

once color or texture is introduced into perception for a manufacturing application, there are likely to be

existing, successful machine vision approaches for object identification.
18 

Table 3.3. Surface Appearance Metrics. 

Metric Metric

1 Reflectance Bidirectional reflectance distribution function (BRFD)

2 Object material As given in object description

3 Color Metric is appropriate color or radiometric space; possibly sensor dependent

4 Texture Many possible structural, statistical and power spectrum metrics

4 Creation of an Object Database

The calculation of the proposed metrics for an object requires a 3D representation of that object. An 

initial strategy was to try to obtain CAD models of engine parts (from older or discontinued auto models) 

from the various automobile manufacturers or from free sources on the web. Both Ford Motor Company 

and General Motors were contacted, and unfortunately, this strategy was not viable due to proprietary 

issues. The latter option of finding engine parts on the web required developing a list of engine part 

names and few, free CAD models of engine parts were found. 

An alternative was to use the models available in the Purdue Engineering Shape Benchmark (ESB) 

(https://engineering.purdue.edu/cdesign/wp/) database that were deemed similar to engine parts. The 

database contained images of the part, an OBJ file for the part, and a mesh of the part in STL format. A 

subset of about 200 objects from the over 900 objects were selected from the ESB database. Metrics 

based on geometry were calculated for the selected parts. However, the results from the curvature 

algorithm did not yield rational results. The reason for this was because a finer mesh was required. An 

attempt was made to create finer meshes of the parts using the OBJ files of the objects that were available 

from the Purdue ESB database, but we were unable to open these files with any of the commercially 

available software that we had. 

As a result, another web search of freely available CAD models was conducted. This search yielded over 

a hundred parts from the following website: www.GrabCAD.com. The restriction of parts associated 

with automobile engine parts and the availability of usable file formats (i.e., file formats for which the 

authors had software to open the files), limited the selection of objects. As stated in Section 3, objects 

that fit within a (50 x 50 x 50) cm volume were used in the analysis. 

Another option that arose was the purchase of CAD models, such as of an automotive engine. However, 

there were a few of drawbacks to this option: cost, procurement time, and type of file. The cost was not 

prohibitive as CAD models of an engine are available for about $600. The files for the parts were meshed 

files, and they did not appear to be fine meshes. This issue may have been resolved by requesting the 

polygonal models of the parts, which would allow us to re-mesh to finer meshes, but we did not get a 

response from the creator of the mesh files. 

Therefore, the objects used for testing the metrics and classification system were those obtained from the 

GrabCAD website and are given in Appendix A. One hundred and thirty-three (133) objects were 

downloaded; however, two of the objects could not be meshed and curvature metrics could not be 

performed for another 15 of the objects. There are some known bugs in the curvature algorithm and 
19 

further debugging of the algorithm was not pursued as this was beyond the scope of this effort. This 

reduced the object database to 116. Six of the objects had at least one dimension larger than 50 cm. These 

objects were left in the database as it did not have a significant effect on the manual classifications or the

cluster-based classifications. However, when plotting the metrics for the High/Low observations, the 

metrics for the six oversized objects were excluded; thus, these observations were based only on objects

that were (50 x 50 x 50) cm or smaller. 
20 

5 Computation of Metrics

Different metrics characterizing an object were computed using a triangulated mesh of the object. 

Meshes of the objects, in STL format, were created from CAD models of the objects. The STL files were 

then converted to PLY (Polygon File Format) files. A direct generation of PLY files from the CAD 

models was not done as the generated PLY meshes were not always triangulated. The conversion from 

STL to PLY format was done to remove duplicate nodes. 

The mesh files (in PLY format) were processed using a custom script written in MATLAB. Some 

functions used in the script were downloaded from the publicly available toolbox_graph which contains 

procedures for processing mesh data, http://www.mathworks.fr/matlabcentral/fileexchange/5355-toolboxgraph/content/toolbox_graph/html/content.html (last accessed: 08/30/13). Below are two lists of metrics: 

a list of primary characteristics calculated directly using the mesh of an object and a list of characteristics 

derived from the primary characteristics. Each metric is briefly described below. 

A. Primary characteristics

1) Total surface area of an object: this is the sum of the areas of all triangles. The area of a 

single triangle was calculated as one half of the length of the cross product of two vectors 

forming two sides of a triangle. NOTE: the surface of the selected objects (see Section 4) had 

to be represented by one continuous and closed mesh. This restriction excludes CAD models 

of objects built from distinct subcomponents with more than one surface. 

2) Total volume of an object: the algorithm is based on the method described in Zhang and Chen 

(2001). NOTE: the function which calculates the volume assumes that all normals are 

correctly oriented, i.e., pointing outward. 

3) X, Y, Z extents (DX, DY, DZ): The maximum extents along the x-, y- and z-axes in which 

the CAD model was created. NOTE: the three extents are not necessarily equal to the 

dimensions of the bounding box containing the object. However, in most cases, the 

coordinate frame of the CAD model is aligned with the natural directions associated with the 

object, e.g., axes of symmetry or three longest edges.

4) Area of the convex hull. The MATLAB function convhull() was used to generate a mesh 

representation of the convex hull of the object. The total surface area of the convex hull was 

then computed using the same procedure used to compute the total surface area. 

5) Volume of the convex hull. The same algorithm used to compute the total volume was used 

on the mesh created with MATLAB function convhull() to obtain the convex hull volume. 

6) Fraction of an object’s surface area having a given shape type. Shape type is determined 

from the principal curvatures (cmin, cmax) computed at a node. The principal curvatures for the 

six shape types are given in Table 5.1. In Table 5.1, the notation within the parentheses 

indicate whether (cmin, cmax) are positive, negative, or zero. 
21 

Table 5.1. Shape types and associated principal curvatures.

Cap (+, +) Cup (-, -) Saddle (-, +) 

Ridge (0,+) Rut(-,0) Flat (0,0) 

The above images were obtained from http://radiographics.rsna.org/content/22/4/963/F18.expansion.html.

The curvature tensor was calculated by calling the function compute_curvature() from 

toolbox_graph. This function calculates the tensor at every vertex. Then, the curvature tensor 

for a triangle is calculated as the average of the tensors for the three vertices that define the 

triangle. The shape type of a triangle is determined by the average tensor. The area of all 

triangles with the same shape type are summed up and normalized by the total surface area of 

the object. The algorithm for calculating the curvature is based on the method developed by 

Alliez et al. (2003) and Cohen-Steiner and Morvan (2003). The method calculates the 

angular difference between the normals of all triangles which share the same vertex for which 

the curvature tensor was calculated. 

NOTES: i) The computed curvatures will likely not have values exactly equal to zero, i.e., a 

flat surface. Therefore, a parameter called the flatness threshold was defined to determine 

whether the vertex was on a flat region or not. A meshed cube, sphere, and cylinder were 

used in simulations to determine a value for the flatness threshold. Based on the simulations, 

the flatness threshold value was set to 0.001. ii) Principal curvatures have dimension of 

(1/length) and are sensitive to scale. However, the function compute_curvature() outputs 

results which are scale invariant because the code normalizes the length of each triangle edge 

by the average length of all edges (for example, the curvatures of a sphere do not depend on 

the radius of a sphere). Normalization does not affect the shape type classification – in fact, 

normalization bounds the calculated curvatures for all the objects in a narrow range, making 

it easier to determine the flatness threshold. iii) The function compute_curvature() may 

sometimes fail as it did in 15 of 131 cases. The reason for this is unknown and this bug was 
22 

reported a few years ago but was not fixed4

. iv) Since the mesh obtained from a CAD model 

does not contain any noise (only discretization error due to meshing), the parameter 

option.curvature_smoothing, in the function compute_curvature(), was set to 1. Basically, 

this means that no averaging was applied.

7) Total length of sharp edges. An edge is classified as sharp if the directions of the two 

normals of the adjacent triangles differ by more than 45°. The reported value is the sum of 

all sharp edges divided by the sum of the maximum extents (calculated in 3 above). 

Although, this metric is not in Table 3.1, we could easily calculate this metric since we 

calculated the shape type in (6) and we felt that it could be a useful metric. For laser-based 

perception systems, a higher value for this metric may indicate potentially noisier data due to 

edge effects (i.e., splitting of the laser beam at edges).

 

NOTE: normalization makes the comparison between different objects scale invariant, for 

example the normalized length of a cube is 4, regardless of the size of the cube. The 

normalized lengths for some geometrical primitives are given in Table 5.2. 

Table 5.2. Normalized length of sharp edges for some geometrical primitives.

Geometrical primitive Value

Sphere 0 

Cube 4 

Cylinder

with diameter D and height H

π

�1 + H

2D�

Cylindrical ring

with inner diameter Din , and outer 

diameter Dout , and height H

2 π � Din

Dout

+ 1�

�2 + H

Dout

�

Circular cone

with diameter D and height H

π

�2 + H

D�

Square pyramid

with side L and height H

4 �1 + ��

H

L

�

2

+ 0.5 �

�1 + H

L

�

B. Derived characteristics 

1.) In the literature, we found three definitions for compactness (we used all three definitions in 

this study): 

a. Volume/Surface area

 

4 See http://stackoverflow.com/questions/12922419/rectifying-compute-curvature-m-error-in-toolbox-graph-inmatlab and http://www.mathworks.com/matlabcentral/fileexchange/5355-toolbox-graph, Post 03 Mar 2009 by 

David S.
23 

b. Max extent/Min extent

c. Convex hull area3

/Convex hull volume2

2.) Density = (1- object volume/convex hull volume) 

3.) Smoothness 

a. Hull crumpliness = Object surface area/Convex hull area

b. Crinkliness = Surface area/(Surface area of a sphere with the same volume as the object) 

4.) Aspect ratio

a. DX/DY

b. DX/DZ

c. DY/DZ

The above metrics were calculated for all the objects in Appendix A and the calculated values are 

tabulated in Appendix B. In Table B1, the summation of the values for Cap, Ridge, Cup, Flat, Saddle, 

and Rut should equal 1 as the values represent the fraction of the object that is considered to be cap, cup, 

flat, ridge, rut, or saddle. 

The metrics associated with symmetry were not computed because we could not find algorithms to 

adequately quantify symmetry. We also felt that the reason symmetry is important to perception is 

because objects that are more symmetric result in more pose ambiguities than asymmetric objects. 

Therefore, the metric “unique views” would be able to capture that aspect of an object without having to 

compute the “symmetry” of the object. Also, the number of significant features was not computed due to 

time constraints. Topological features such as the number of holes was also not obtained due to: 

• Definition of a hole: would a hole that did not go entirely through the object be considered a 

hole? For perception systems, an incomplete hole can appear the same as a through hole, but 

topologically is not the same.

• Size of hole. If a perception system could not identify a hole due to poor resolution, or the hole is 

not readily sensed from the exterior, then would the number of holes be a relevant metric? 

• Hole count is global. The topological number of a shape is a global feature that may not be sensed 

from any particular sensor view.
24 

6 Classifications

There were several different methods used to classify the objects in the database given in Appendix A 

using the metrics described in Section 5. The two main methods for classification used in this work were 

manual (Section 6.1) and algorithmically-based (Section 6.2). Since classification methods rely on a set 

of parameters to characterize an object, a manual classification system was felt to yield a better system 

since it is difficult to develop classifiers that encompassed prior knowledge, experience, and intuition. 

However, this method is very subjective and may be difficult for more complex objects, which may create 

ambiguities when determining how to classify an object. An algorithmically-based method would be 

more objective but requires time and effort to develop. 

6.1 Manual Classification 

Three approaches were considered for the manual classifications. These approaches are described in the 

following sub-sections.

6.1.1 Geometric Approach

This approach involves classifying objects based on their geometry where similar shaped objects were put 

into the same class. The objects were grouped based on viewing a 2D image of the object and other 

information regarding scale or size was not considered. The obvious drawback to classifying objects 

based on geometry is that many objects are a combination of various basic geometric shapes and 

judgment will have to be depended upon. 

The objects from the database were placed into six classes, A to F, and the groupings are given in Table 

6.1. In general, the objects in Classes A to F consisted of:

• Class A - flat and thin (high aspect ratio) objects; objects that were “2D” or planar

• Class B – gears, wheels, or round objects

• Class C – bulky or block-like objects 

• Class D – rounded/curved objects that did not fit into Class B

• Class E – objects made with flat, thin material; objects similar to Class A but that are “3D” (e.g., 

bracket). Objects in this class are also more angular than those in Class D.

• Class F – cylindrical or tubular type objects

Once the classification was performed, bar plots of each metric (surface area, volume, etc.) were 

generated. Two of these plots are shown in Figure 6.1. The plots were made to determine if there was

any clustering of the metrics for a given class. For example, from visual inspection, two general 

observations based on Figure 6.1 are that, on average, objects in Class C have higher volumes, and that 

the compactness (defined as the ratio of maximum extent to minimum extent of an object) for objects in 

Class A were higher than those in the other classes. These observations are noted in Table 6.1. An 

observation of High/Low was made only if it was clearly evident in the plot; if there was no clear 

evidence, no observation of High/Low was noted for the metric (see Figure 6.2). As this is a visual 

observation, the determination of High/Low is subjective. These plots were generated for all 

classifications – manual and algorithmic based. 
25 

a. Volume b. Compactness: Max extent/Min extent

Figure 6.1. Plots of (a) Volume and (b) Compactness for objects in classes A to F. 

Figure 6.2. Plot of the Saddle metric shows no clear indication of High/Low for a given class. 

An objective way to determine whether a metric was High/Low for a given class would be based on the 

comparison of the statistical averages for each class for a given metric. However, the standard deviations 

of the average for many of the classes are large (in some cases extremely large) indicating that the 

observations based on the average would not be statistically significant. Thus, this method was not used. 
26 

Table 6.1. Classification based on object geometry. 

Class A (thin, flat objects – “2D” objects)

HIGH: 

• compactness (max/min 

extent)

• compactness (CH 

area3

/CH volume2) 

• aspect ratio 

LOW: 

• crumpliness

• ridge

• cup

Class B (gears, wheels, round objects)

HIGH: 

• length of sharp edges

LOW: --- 

Class C (bulky or block-like objects)

HIGH: 

• surface area

• volume

• convex hull volume

• compactness

(volume/surface area)

• cup

LOW: --- 

Class D (round objects that did not fit in Class B)

HIGH: --- 

LOW: 

• volume
27 

Class E (thin, flat objects that are “3D”)

HIGH: 

• convex hull volume

• density

• crinkliness

• flat

LOW: 

• compactness 

(volume/surface area)

• ridge

• saddle

• rut 

• cup

Class F (cylindrical, tubular objects)

HIGH: 

• volume

• convex hull volume

• cap

• ridge

• cup

LOW: 

• flat

6.1.2 Laser-based Technology Approach 

This approach grouped the objects in the database based on how difficult it would be for a particular type 

of perception system to obtain the pose of the object given certain conditions. The objects were placed 

into one of five levels (i.e., 5 classes) of difficulty as follows: 

Levels of Difficulty

1 – Very Easy: All 6 DOF (degree of freedom; 3 positional and 3 rotational) can be obtained 

with relatively high accuracy

2 – Easy: All DOF can be obtained, but with relatively low accuracy 

3 – Medium: Only 4 or 5 of the DOF can be obtained with relatively high accuracy

4 – Hard: Only 4 or 5 of the DOF can be obtained, but with relatively low accuracy 

5 – Very Hard: Only the 3 positional DOF can be obtained 

In order to aid in gauging the difficulty of measuring an object’s pose using a certain perception system, 

three additional metrics were defined for an object: 1) Pose Unambiguity, 2) DOF Needed, and 3) 

Ambiguous DOF Needed. Definitions for these metrics and possible values for them are presented below.
28 

Pose Unambiguity: Measure of how many degrees of freedom can be determined unambiguously for an 

object when all relevant features are visible.

3 – Only a 3DOF position can be calculated unambiguously 

4 – Only a 4DOF pose can be calculated unambiguously 

5 – Only a 5DOF pose can be calculated unambiguously 

6 – No ambiguity, full 6DOF pose can be obtained unambiguously 

DOF Needed: Number of degrees of freedom that must be calculated in order to properly assemble the 

object into a larger assembly. Although in some cases, some of the degrees of freedom may remain 

ambiguous (e.g., differentiating between the front and back face of a flat washer) that degree of freedom 

may still need to be calculated in order to assemble the object (e.g., an assumption must be made about 

which is the front side of a flat washer in order to calculate its two angles of rotation which will allow a 

robot to insert a screw through it). 

3 – Only a 3DOF position must be calculated (e.g., ball bearing) 

4 – 4DOF must be calculated

5 – 5DOF must be calculated

6 – All 6DOF must be calculated

Ambiguous DOF Needed: Number of ambiguously-defined DOF that need to be calculated. This is the 

difference between DOF Needed and Pose Unambiguity. 

For each object in the database, values for the above three metrics were first assigned.

Perception Systems

For this approach, the perception systems for which the object pose determination difficulty would be 

gauged had to be defined. To do this, a perception system was defined as a combination of four factors: 

1) technology, 2) clutter, 3) background, and 4) presentation. Definitions for these four factors and 

possible values for them are explained below. 

Technology: Sensor hardware is based on: 

1) a laser line scanner mounted on a 6DOF arm, 

2) a multiple camera machine vision system in which one or more of the cameras are 

mounted on a 6DOF arm, 

3) a structured light area scanner mounted on a 6DOF arm, or 

4) a combination of laser line scanner, structured light area scanner and machine vision in 

which the object is manipulated with a gripper in order to present the object more 

favorably to one or more of the sensors. 

Clutter: Object is 1) isolated or 2) there are other identical objects in the field-of-view of the 

sensor(s).

Background: Object is 1) on a flat surface or 2) in a bin. 

Presentation: Object is presented to the sensor(s) 1) in a favorable orientation or 2) with 

important features occluded.
29 

Using the above factors, a perception system may be described using four numbers. For example, System 

1111 means a perception system using a laser line scanner to determine the pose of an isolated object on 

a flat surface presented in a favorable orientation. Similarly, a System 1221 means a perception system 

using a laser line scanner to determine the pose of an object in a bin with other identical objects, and

presented in a favorable orientation (e.g., at the top of the pile anywhere in the bin with relevant features 

visible).

Assumptions

In order to gauge the difficulty of a certain perception system’s ability to determine the pose of an object, 

several assumptions regarding the object, its environment, and the perception system itself were made. 

These assumptions are presented below.

1. The object is stationary. 

2. The object material, color, and texture are favorable to the technology being used.

3. Lighting conditions are favorable to the technology being used. 

4. The environment is stable throughout the perception task. 

5. Perception systems that are based on machine vision technologies have a higher resolution than 

those that are based on laser line scanning technologies and therefore, can more accurately 

measure the poses of smaller objects.

6. Perception systems that are based on laser scanning technologies can more accurately measure 

the pose of volumetric objects (i.e., objects with features in all three dimensions as opposed to flat 

objects) than perception systems that are based on machine vision technologies. 

7. Perception systems that use structured light area scanning technologies or a combination of laser 

line scanning and machine vision inherit the best characteristics of the laser line scanning- and 

machine vision-based perception systems.

8. All the perception systems use optimized algorithms (e.g., data processing, filtering, fitting, etc.) 

in order to calculate the poses of objects using the raw sensor data.

9. Perception systems that use laser line scanning and structured light area scanning technologies 

yield more accurate poses of objects that are presented among many other identical objects (i.e., 

cluttered background) because it is easier to isolate (segment) the data from a single object among 

many identical objects using 3D data.

Placing the object in a bin with other identical parts and in a favorable orientation adds one level of 

difficulty to each kind of perception system used with the same object isolated on a flat surface. 

Theoretically, the above method can result in many possible combinations of factors, which could define 

a large number of perception systems. For the purposes of this classification, only six different systems 

(1111, 1221, 2111, 2221, 3111, and 3221) were considered. For Presentation, only the case of favorable 

orientation (represented by the fourth digit in the nomenclature with a value = 1) was used as the 

alternative of 2 (important features occluded) would yield numerous classifications depending on which 

features were occluded. 

The classification for Systems 1111, 2111, and 3111 are given in Tables 6.2 to 6.4. Systems 1221, 2221, 

and 3221 are not shown as they are similar to Systems 1111, 2111, and 3111, respectively; the only 

change being the difficulty levels for 1221, 2221, and 3221 were increased by 1 (i.e., the classes increased 
30 

by 1). No difficultly level was higher than Class 5 – Very difficult. For example, for System 1111, two 

objects were placed in Class 5. For System 1221, this meant that the difficulty level would have been 

Class 6, but since Class 5 was the highest level, these two objects in Class 5 for System 1111 were placed 

into Class 5 for System 1221. 

As mentioned earlier, High/Low observations were made based on bar plots of each of the metrics. 

However, in a couple of classes (System 1111 - Class 5 and System 3111 - Class 3), there were only two 

objects in that class. Therefore, the addition of one or more objects could potentially reverse or nullify 

the High/Low observations, i.e., these observations have a low level of confidence associated with them.
31 

Table 6.2. Classification for System 1111: Technology = laser line scanner mounted on 6DOF 

arm, Clutter = isolated, Backround = on flat surface, Presentation = favorable orientation.

System 1111: Class 1 – very easy 

HIGH: 

• surface area

• volume

• convex hull area

• convex hull volume

• compactness (max 

extent/min extent)

• compactness (CH 

area3

/CH volume2) 

• aspect ratio 

LOW: --- 

System 1111: Class 2 – easy

HIGH: 

• aspect ratio 

LOW: --- 
32 

System 1111: Class 3 - medium

HIGH: --- 

LOW: --- 

System 1111: Class 4 – hard

HIGH: --- 

LOW: 

• surface area

• volume

• convex hull area

• convex hull volume

• compactness 

(volume/surface area)

• compactness (max 

extent/min extent)

• compactness (CH 

area3

/CH volume2) 

• aspect ratio

System 1111: Class 5 – very hard

HIGH: --- 

LOW: 

• surface area

• volume

• convex hull area

• convex hull volume

• compactness 

(volume/surface area)

• compactness (max 

extent/min extent)

• compactness (CH 

area3

/CH volume2) 

• aspect ratio
33 

Table 6.3. Classification for System 2111: Technology = multiple camera machine vision 

system in which one or more of the cameras are mounted on a 6DOF arm, Clutter = isolated, 

Backround = flat surface, Presentation = favorable orientation.

System 2111: Class 1 – very easy 

HIGH: 

• surface area

• volume

• convex hull area

• convex hull volume

• compactness (max 

extent/min extent)

• compactness (CH 

area3

/CH volume2) 

• flat

• aspect ratio

LOW: 

• ridge

System 2111: Class 2 - easy

HIGH: --- 

LOW: 

• compactness 

(volume/surface area)
34 

System 2111: Class 3 - medium

HIGH: 

• cap

• ridge

LOW: 

• compactness (max 

extent/min extent)

• compactness (CH 

area3

/CH volume2) 

• flat

• cup

• aspect ratio

System 2111: Class 4 – hard

No objects were placed in this class. 

System 2111: Class 5 – very hard

No objects were placed in this class. 
35 

Table 6.4. Classification for System 3111: Technology = structured light area scanner 

mounted on a 6DOF arm, Clutter = isolated, Backround = flat surface, Presentation = 

favorable orientation.

(System 3111: Class 1 – very easy

HIGH: 

• surface area

• volume

• convex hull area

• convex hull volume

• compactness 

(volume/surface area)

• compactness (max 

extent/min extent)

• compactness (CH 

area3/CH volume2) 

• flat

• aspect ratio 

LOW: 

• ridge
36 

System 3111: Class 2 - easy

HIGH: --- 

LOW: 

• surface area

• volume

• convex hull area

• convex hull volume

• cup

• aspect ratio

System 3111: Class 3 - medium

HIGH: --- 

LOW: 

• surface area

• volume

• convex hull area

• convex hull volume

• compactness (max 

extent/min extent)

• compactness (CH 

area3

/CH volume2) 

• saddle

• aspect ratio

System 3111: Class 4 – hard

No objects were placed in this class. 

System 3111: Class 5 – very hard

No objects were placed in this class. 

6.1.3 Vision-based Technology Approach 

This approach attempts to classify the objects for vision-based perception systems using the following 

criteria for obtaining pose in the openCV (Bradski and Kaeber, 2008) and the Point Cloud Libraries

(Rusu, 2011): 

1. Quality and quantity of an object's perception features

2. Complexities of algorithms to compute those features 

3. Uniqueness of those features from different perceptive views

Based on the above criteria, each object was placed into 10 levels. The criteria for the pose score are: 

• Score 1 & 2: If all of the following are true:

o the object has no unique features in all views; 

o it is difficult to obtain visual features of the object (e.g., small holes in the object); 

o the object features are quadratic or higher order.

• Score 3 & 4: if all of the following are true:
37 

o the object has at least one medium unique feature (e.g., feature cannot be easily detected) 

in one to two views;

o one to two linear features (e.g., line, edge, point, corner). 

• Score 5 & 6: if all of the following are true:

o the object has at least one good unique feature (e.g., feature can easily be detected) in 

three to four views;

o three to four linear features.

• Score 7 & 8: if all of the following are true:

o the object has at least one excellent unique feature (e.g., feature is very easily detected) 

in five to six views;

o five to six linear features.

• Score 9 & 10: if all of the following are true:

o the object has several excellent unique features in all views;

o many linear features.

The following procedure to classify the 116 objects into 10 classes: 

1. Load the CAD file of each object into MeshLab software

2. View the object from the top, bottom, left, right, front, and back. From these views, the quantity 

and quality of the features as well as their uniqueness were determined. 

3. Based on Step 2, assign a pose score to the object. 

4. Group objects with the same pose score into a class: Pose score 1 = Class 1, etc.

For objects in Classes 1 to 4, it would be very problematic for the perception systems to determine their 

poses. Perception systems would have very little problems in accurately measuring the poses of objects 

in Classes 7 to 10. 
38 

Table 6.5. Vision-based Perception System Classification Approach. Class 1 = very difficult, Class 

10 = very easy.

Class 1 HIGH: --- 

LOW: 

• surface area

• volume

• convex hull area

• convex hull volume

• rut 

Class 2 HIGH: --- 

LOW: 

• surface area

• volume

• convex hull area

• convex hull volume

• cup

Class 3

HIGH:

• cup

LOW: --- 

Class 4

HIGH: --- 

LOW: --- 
39 

Class 5

HIGH: 

• cap

LOW: --- 

Class 6

HIGH: --- 

LOW: 

• compactness (max 

extent/min extent)

• compactness (CH 

area3

/CH volume2) 

• aspect ratio

Class 7

HIGH: --- 

LOW: --- 

Class 8

HIGH: --- 

LOW: 

• cup

Class 9

HIGH: --- 

LOW: --- 
40 

Class 10

HIGH: --- 

LOW: --- 

6.2 Classification based on Clustering

We used the metrics given in Table B1 for clustering. Clustering, in this work, is the process of 

organizing a set of 3D CAD models into groups in such a way that the 3D models within the group are 

more similar to each other than they are to other objects belonging to different groups. Clustering is also 

known as an unsupervised learning technique in the scientific literature. We use k-means cluster analysis 

(Teknomo and Kardi, 2006) along with the shape metrics and a user-defined number of clusters to 

classify the 3D CAD models. We assume that the models as represented by the shape metrics would 

allow us to distinguish one group from another. 

The k-means algorithm is an algorithm to cluster n objects based on attributes into k partitions, k < n. It is 

similar to the expectation-maximization algorithm for mixtures of Gaussians in that they both attempt to 

find the centers of natural clusters in the data, where there are k clusters. In this work, we used k = 5, k = 

6, and k = 10 as these were the number of classes used for the manual classifications. The results of the 

clustering based on k = 5, k = 6, and k = 10 are shown in Table 6.6, Table, 6.7, and Table 6.8, 

respectively.

The metrics we used for k-means clustering are only based on shape type (see Section 5, Table 5.1). The 

other metrics were not used since there is a large variation in the size of the different models and most of 

the other shape metrics are scale dependent.
41 

Table 6.6. k-means clustering with k = 5 using the shape index metrics.

k = 5: Class 1 

HIGH: 

• flat

• aspect ratio

LOW: 

• cap

• ridge

• saddle

k = 5: Class 2 

HIGH: 

• aspect ratio

LOW: --- 

k = 5: Class 3 HIGH: 

• ridge

• cup

LOW: 

• surface area

• volume

• convex hull area

• convex hull volume

• compactness (max 

extent/min extent)

• compactness (CH 

area3

/CH volume2) 

• crumpliness

• flat

• cup
42 

k = 5: Class 4

HIGH: 

• rut 

LOW: 

• compactness (max 

extent/min extent)

• compactness (CH 

area3

/CH volume2) 

• aspect ratio

k = 5: Class 5 HIGH: 

• cap

• saddle

LOW: 

• surface area

• volume

• convex hull volume

• cup
43 

Table 6.7. k-means clustering, k = 6 using the shape index metrics.

k=6: Class 1 

HIGH: --- 

LOW: --- 

k=6: Class 2

HIGH: 

• surface area

• volume

• convex hull area

• convex hull volume

LOW: --- 

k=6: Class 3 [Subset of Class 4, k=5] HIGH: 

• surface area

• convex hull volume

• rut 

LOW: 

• compactness 

(volume/surface area)

• compactness (max 

extent/min extent)

• compactness (CH 

area3

/CH volume2) 

• flat

• aspect ratio
44 

k=6: Class 4 [Same as of Class 3, k=5] HIGH: 

• ridge

LOW: 

• surface area

• volume

• convex hull area

• convex hull volume

• crumpliness

• flat

• rut 

• cup

• length of sharp edges

• aspect ratio

k=6: Class 5 [Subset of Class 1, k=5] HIGH: 

• compactness (max 

extent/min extent)

• compactness (CH 

area3

/CH volume2) 

• flat

• aspect ratio

LOW: 

• cap

• ridge

• rut 

• cup

k=6: Class 6 [Same as of Class 5, k=5] HIGH: 

• compactness (max 

extent/min extent)

• compactness (CH 

area3

/CH volume2)

• cap

• saddle

LOW: 

• rut 

• cup
45 

Table 6.8. k-means clustering, k = 10 using the shape index metrics.

k=10: Class 1 [Subset of Class 5, k=5] HIGH: 

• cap

• saddle

LOW: 

• surface area

• volume

k=10: Class 2 

HIGH: 

• aspect ratio

LOW: --- 

k=10: Class 3 [Subset of Class 1, k=5] HIGH: 

• flat

• aspect ratio

LOW: 

• saddle

• cup

k=10: Class 4 [Subset of Class 1, k=5] HIGH: 

• flat

LOW: 

• compactness 

(volume/surface area)

• ridge

• saddle

• rut 

• cup

k=10: Class 5 [Subset of Class 2, k=5] HIGH: 

• compactness 

(volume/surface area)

• ridge

LOW: --- 
46 

k=10: Class 6 [Subset of Class 4, k=5] HIGH: 

• rut 

LOW: 

• cap

k=10: Class 7 [Subset of Class 4, k=5] HIGH: 

• ridge

• rut 

• cup

LOW: 

• compactness 

(volume/surface area)

• compactness (max 

extent/min extent)

• compactness (CH 

area3

/CH volume2) 

• flat

• aspect ratio

k=10: Class 8 HIGH: --- 

LOW: 

• cap

• ridge

• saddle

k=10: Class 9 

HIGH: 

• cup

LOW: --- 
47 

k=10: Class 10 [Same as Class 3, k=5] HIGH: 

• cap

• ridge

LOW: 

• surface area

• volume

• convex hull area

• convex hull volume

• flat

• rut 

• cup

• length of sharp edges

• aspect ratio

 
48 

7 Discussion and Summary

7.1 Discussion

As can be expected, manual classifications will be subjective and will likely lack consistency as 

evidenced by the classifications in Section 6.1. The subjectivity and lack of consistency may be mitigated 

by training and developing guidelines/rules for performing the classification. 

An objective method to classify objects could be one that is based on metrics characterizing an object. 

Advantages of such a method are objectivity and ease of implementation. The disadvantages of this 

method are: 

1. Selection and determination of an appropriate set of metrics, 

2. Classifications may change if different metrics were used. For example, given an object, the 

object may be placed in Class 1 using Metrics Set A or it may be placed in Class 2 if Metrics Set 

B were used, 

3. Classifications may change if parts are added to or removed from the population of parts. 

Clustering methods are based only on the relative similarity of dataset attributes to an aggregate 

cluster average, and outliers and subsequent changes to the attribute space may cause shifts in 

cluster centroids, 

4. Development of algorithms to quantify the metric. For example, quantifying symmetry is very 

difficult as discussed in Section 3. Others metrics that would be hard to quantify algorithmically 

include the number of stable of poses and the number of unique views, and

5. Requirement of a 3D model of the object. 

The classifications using cluster analysis (Section 6.2) were performed using only the shape type metrics. 

For the algorithmic-based approach, the number of classes can be set to any number. To reduce the 

variables between the algorithmic and the manual approaches, the same number of classes, 5, 6, and 10 

used in the manual approaches, were used in the algorithmic-based approach. However, since the criteria 

for the classifications were different (e.g., geometry based, technology based, shape type) the resulting 

classifications would not be expected to be similar. 

Many methods for clustering are found in various communities. Besides the k-means cluster analysis, we 

also tried a very common approach to clustering called the hierarchical method (Johnson, 1967), also 

known as Agglomerative clustering. This method is very popular in areas of data mining and 

bioinformatics. In hierarchical clustering, we do not need to know the number of clusters/groups ahead of 

time; i.e., the 3D CAD models are not divided into predefined numbers of clusters. We then use a 

Dendrogram, which is a visual representation of hierarchical data to show the clusters. The Dendrogram 

tree starts at the root, which is at the top for a vertical tree (the nodes represent clusters). Figure 7.1 

shows the Agglomerative clustering based on the shape type metrics only with the number of clusters k = 

30. 
49 

Figure 7.1 Agglomerative clustering based on model shape type metrics (number of clusters k = 30). 

In Fig. 7.1, the number of clusters will vary depending on the y value selected. Figure 7.2 shows the 

clusters for y ≈ 1.1. 

Figure 7.2. Agglomerative clusters for y ≈ 1.1. 
50 

One other approach for classification is to use a classifier such as a Support Vector Machine (SVM) 

(Hearst et al., 1998) classifier that is trained by human-generated training examples to classify a test 

dataset. Other possible classifiers than can be used for classification include neural networks (Funahashi, 

1989), naive Bayes classifiers (Kohavi, 1996), and boosted decision stumps (Qu et al., 2002). 

The High/Low observations in Section 6 seem to indicate that the density, crumpliness, crinkliness, and 

length of sharp edges metrics may not be useful as distinguishing/discriminating metrics for the set of 

objects used in this effort. The area, aspect ratio, cap, compactness, convex hull area, convex hull 

volume, cup, flat, ridge, and volume metrics may be useful as distinguishing/discriminating metrics. 

7.2 Summary and Future Work

This study documented the process to develop a classification system for objects. The purpose of the 

classification system was to support the evaluation of perception systems used for identifying and 

locating static manufacturing parts. The existence of a robust object classification system may eventually 

lead to the development of standard reference artifacts of objects in the various classes. A literature 

review indicated that many of the classification systems developed were for object retrieval and 

manufacturing systems/process and a classification system such as that envisioned for this study does not 

exist. 

In this study, two approaches, manual and algorithm-based, were used to develop a classification system. 

Three manual approaches for the classifications were developed where the criterion for one was object 

geometry and the criteria for the other two were based on the perceived difficulty that a perception 

system, laser-based and vision-based, would encounter when measuring the pose of the object. The 

algorithmic approach involved using cluster analysis to classify the objects based on a set of metrics.

A review of metrics used by other researchers was conducted and a set of metrics was selected for use in 

this study. Commercially or publicly available algorithms were used to calculate the metrics. A database 

of objects was created where the objects in the database were narrowed down to mainly automotive 

engine parts and where a 3D CAD model of the object was freely available. In addition to the three 

manual classifications, k-means clustering was used to generate an additional three classifications where k

was set equal to 5, 6, and 10 using the calculated metrics for shape type.

Based on this work, developing a classification system such as that proposed in this effort will not be 

easily accomplished as the problem involves a huge, multidimensional parameter space. However, the 

experience gained from this work with metrics, algorithms to calculate the metrics, file formats, and 

object databases will benefit future efforts in dealing with smaller object spaces for more defined 

applications. Also, the experience will inform other efforts to design artifacts and experiments for object 

identification and pose estimation. 

The next step for this study would be the determination of whether the classification systems in Section 6

are good or bad through experimental testing using various perception systems. A good classification

would be one that groups objects into classes for which perception systems would yield similar results for 

a given class. For example, a classification system could group a set of objects into three classes where

the measured positional error for the objects would range from (0 to 10) mm, (11 to 20) mm, and (21 to 

30) mm for Class 1, 2, and 3, respectively. An ideal classification system would yield positional errors 
51 

that are within the specified bounds for all objects in that class and for all perception systems. A good 

classification system would yield positional errors that are within the specified bounds for most of the 

objects in that class and for most perception systems. A bad classification system would yield positional 

errors that are outside the specified bounds for the majority of the objects in a given class and for all 

classes. That is, for more than 50 % of the objects in Class 1, the errors would be greater than 10 mm and 

similarly for objects in Classes 2 and 3.

Evaluation of a classification system requires a set of objects and a perception system. For a given set of 

objects and a given perception system, the classification system may be deemed good. However, 

robustness of the classification system is of critical importance – would the classification system fail if 

other objects were added or if another perception system were used? Also, as stated earlier, metrics for 

symmetry and the number of significant features were not used in the cluster analysis in this effort. A 

next step would be to calculate these metrics (and/or other metrics such as number of unique views or 

color) and determine how the classifications would change and to evaluate the classification system 

through experimental testing.

If a classification system is deemed bad, the reasons for its failure need to be determined; reasons such as

(1) were the metrics not the appropriate ones? and (2) was the classification system only valid for a 

particular type of perception system technology? 
52 

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54 

Appendix A: Objects Used in Classification Systems

The objects selected for use in the classification system were downloaded from www.GradCAD.com and 

images of these objects are given in the table below. The object file names are given below each image, 

and they indicate the format of each file: SLDPRT = SolidWorks; STP/STEP = Step; IGS/IGES = IGES; 

3DM = Rhino; DWG = AutoCAD. 

The objects in red and blue shaded cells were not included in the classification. The cells shaded in red 

could not be meshed. The curvature metrics for objects in cells shaded in blue could not be calculated. 

There are some known bugs in the curvature algorithm and further debugging of the algorithm was not 

pursued as this was beyond the scope of the task. The orange shaded cells were objects which had at least 

one dimension greater than 50 cm. 

Table A.1. Objects used in the classification systems.

1inchCarbSpacer.SLDPRT 4 cylinder engine head 

gasket.SLDPRT 944 Bellhousing 

Base.SLDPRT 944to911OuterCVAdapter.S

LDPRT

9 Blade Impeller.SLDPRT 9 Inch Pin Support.SLDPRT AlumPIPE.SLDPRT Audi20VExhaustFlange.SL

DPRT

Audi bearing retainer 

tool.SLDPRT

Audi-VW Rear crank 

plate.IGS Base Bracket.SLDPRT bearing body.SLDPRT

Bevel Gear.SLDPRT

BigBlockChevyFlange.igs Block.dwg boltnew.SLDPRT
55 

BOVTop-2.SLDPRT BRACKET.SLDPRT brake_shoe.igs BRE 1.4L I4 Needle Sleeve 

Bearing Body.SLDPRT

BSP Tee.IGS

Bus Bar 2 cells 

40152S.SLDPRT Cam retainer.stp camshaft.SLDPRT

Carburator Body.IGS

CastAluminumIntake.SLDP

RT 

CastExhaustCollector.SLDP

RT CetrifugalImpeller.igs

ChevyHeader 

Flange.SLDPRT ClutchCover.SLDPRT ClutchPlate1.igs ClutchPlate2.SLDPRT

Collar 1in Shaft.stp Collar Shaft.SLDPRT Connecting rod.SLDPRT Cover_Plate.SLDPRT

CrankGear.SLDPRT Crankshaft.SLDPRT 

Cylinder Block 

5cyl.SLDPRT Diffuser.dwg
56 

DISC PLATE.SLDPRT ElbowCastIron.SLDPRT 

EngineAirIntake.SLDPRT EngineBlock.stp

EngineBottomPlate.igs

EngineFrontCover.SLDPRT

Engine Gudgeon 

Pin.SLDPRT

Ferrule 2Inch Clamp Tube 

OD w Seal Groove_pt1.3dm

Ferrule 2Inch Clamp Tube 

OD w Seal Groove_pt2.3dm

fitting.3dm Flange.igs Fly wheel.SLDPRT

Ford GT40 intake 

spacer.SLDPRT Fuel Pump Delete Plate.stp

fuelpumpR1.dwg

gasket.SLDPRT

Gear.SLDPRT

Gear1.dwg GearboxCasing.SLDPRT GearBoxPart2.SLDPRT 

GearBoxTophousing.SLDPR

T 

GearHousing.SLDPRT Geneva Cam.SLDPRT GM 3R U-Joint.stp
57 

GMLS6FrtCover.SLDPRT Helical gear wheel.STEP HondaNSR125CylinderHead

Gasket.IGS

Housing.SLDPRT

HousingSquare.SLDPRT IgnitionCoilMazda13B.SLD

PRT

Impeller.SLDPRT IntakeManifold.3dm

IntakeMobil.IGS

(IntakeMobilPart1.stl) IntakeMobil.IGS

(IntakeMobilPart2.stl) IntakePipeComponent.igs IntakeTrumpet.igs

Jetta_Actuator 

Bracket.SLDPRT link.IGS LockNuts.SLDPRT LowerControlArm.stp 

LowerThermostatHousing 

spacer GM.SLDPRT M20LiftingEyeBolt.SLDPR

T

ManifoldPlate.stp MasterCylinder Bracket.3dm

Miata16IntakeFlange.SLDP

RT 

MitsubishiEVOMAPadapter.

SLDPRT

MitsubishiGrandisAirIntake.

stp Needle valve 

screw.SLDPRT
58 

Oerlikon Brake 

valve.SLDPRT OilCoolerBypassCover Plate 

for VW.stp

OilFilter.dwg OilPan.SLDPRT

OilPanModel2.IGS OldhamCoupling.SLDPRT

Parametric Flange.igs

Piston.stp

Piston rod_part1.SLDPRT Piston rod part2.SLDPRT

Pitch2.SLDPRT

PlenumPlate.IGS

Porsche968Flange.SLDPRT

Porsche968IntakeFlange.SL

DPRT

PorscheStrutBarTopBrace.S

LDPRT Pressure plate.SLDPRT

PulleyForAlternator.stp RockerArm.stp

SerratedIntake.SLDPRT SkidPlateBracket.SLDPRT

Socket.SLDPRT SpiralBevelGear.SLDPRT SplitPin.igs

Sproket.SLDPRT
59 

SpurGear.SLDPRT 

SteeringKnuckleFlange 

Spacer.IGS StraightScrewJoint.stp

T3DividedTurboInlet 

Flange.SLDPRT

ThreeTubeJoint.igs Thrust bearing-disc.SLDPRT TowbarElectrics 

Bracket.SLDPRT

Truss Bearing.SLDPRT

Turbo housing.SLDPRT Valve.igs ValveChest.igs ValveClip.SLDPRT

ValveCover2.igs

VariablePitchSpring.SLDPR

T

VW Golf Inlet 

Flange.SLDPRT

W05Lockwasher.SLDPRT

WheelBearingHousingFor a 

VW.stp WINCH MTG 

BRK.SLDPRT

WormGearDesign.SLDPRT WormGear.SLDPRT

wrist pin.SLDPRT

EMPTY EMPTY EMPTY
60 

Appendix B: Calculated Metrics for Objects in Appendix A.

Table B1. Calculated Metrics

FileName Object

ID

Surface

Area

[cm2]

Vol

[cm3]

Extent Convex

Hull

Area

[cm2

] 

Convex

Hull

Vol

[cm3

] 

Compactness

Vol/Surface 

Area

[cm]

Compactness

Max/Min 

Extent

Compactness

CHarea3

/CHvol2

Density

1 – Vol/ChVol DX

[cm]

DY

[cm]

DZ

[cm]

1inchCarbSpacer 1 603 331 15 3 16 639 615 0.549 6.38 688.44 0.46

4cylinderEngineHeadGasket 2 641 44 40 0 17 1308 97 0.069 269.86 238461.05 0.54

944BellhousingBase 3 1307 830 37 2 34 2065 1773 0.635 19.25 2800.11 0.53

944to911OuterCVAdapter 4 373 121 4 11 11 300 338 0.324 2.87 235.50 0.64

9BladeImpeller 5 1 0 1 0 1 1 0 0.024 1.87 178.78 0.45

9InchPinSupport 6 779 549 17 7 17 588 1092 0.705 2.27 170.33 0.50

AlumPIPE 7 1517 301 27 11 17 1080 2470 0.198 2.51 206.58 0.88

Audi20VExhaustFlange 8 558 143 43 9 1 796 287 0.256 53.75 6108.84 0.50

AudiBearingRetainerTool 9 211 94 8 6 8 183 194 0.447 1.38 163.36 0.51

AudiVWRearCrankPlate 10 291 62 15 2 13 379 240 0.214 9.56 938.77 0.74

BaseBracket 11 405 269 14 9 7 387 467 0.664 2.13 265.91 0.42

BearingBody 12 968 908 10 11 23 833 1611 0.938 2.30 222.29 0.44

BevelGear 13 250 116 3 11 11 211 185 0.462 3.94 276.91 0.37

BigBlockChevyFlange 14 488 138 48 8 1 779 324 0.283 50.69 4493.55 0.57

Block 15 271 80 9 6 6 177 187 0.296 1.50 158.12 0.57

BOVTop2 16 153 38 8 2 8 128 73 0.251 4.75 392.98 0.48

BRACKET 17 398 75 10 3 15 394 353 0.188 4.69 491.85 0.79

BRE14LI4NeedleSleeve

BearingBody 18 43 2 2 2 5 35 14 0.045 2.66 217.75 0.86

BusBar2Cells40152S 19 25 2 6 0 2 25 2 0.067 40.73 5254.05 0.06

CamRetainer 20 32 2 7 5 0 51 4 0.066 44.69 8937.25 0.46

camshaft 21 404 193 4 51 4 516 385 0.477 12.50 925.38 0.50
61 

CarburatorBody 22 974 282 9 18 18 725 1378 0.290 2.07 200.83 0.80

CastAluminumIntake 23 525 99 15 10 10 389 499 0.189 1.52 236.53 0.80

CastExhaustCollector 24 361 34 9 6 8 245 291 0.093 1.41 174.61 0.88

CetrifugalImpeller 25 185 21 7 3 7 97 66 0.114 2.10 207.82 0.68

ChevyHeaderFlange 26 554 142 21 5 10 512 646 0.256 4.67 321.56 0.78

ClutchCover 27 1340 248 24 6 24 1130 2028 0.185 4.00 351.20 0.88

ClutchPlate1 28 562 132 15 15 3 390 281 0.235 6.00 754.82 0.53

Collar1inShaft 29 55 12 4 4 1 48 20 0.212 3.50 281.39 0.41

CollarShaft 30 67 14 6 1 6 75 28 0.211 6.00 536.16 0.50

ConnectingRod 31 284 101 18 3 5 264 211 0.355 6.07 412.31 0.52

CoverPlate 32 1454 210 25 11 19 1305 3306 0.144 2.36 203.14 0.94

CrankGear 33 11864 9378 78 7 78 11315 34789 0.790 10.67 1196.91 0.73

Crankshaft 34 759 305 5 9 40 840 1102 0.402 7.99 488.22 0.72

CylinderBlock5cyl 35 7361 3062 49 16 12 3115 9465 0.416 4.12 337.37 0.68

Diffuser 36 1197 511 6 21 21 880 1570 0.427 3.38 276.40 0.67

DISCPLATE 37 692 202 22 1 22 784 279 0.292 28.33 6189.29 0.28

ElbowCastIron 38 2978 2488 23 26 26 2214 7295 0.836 1.17 204.07 0.66

EngineBlock 39 645 132 8 11 11 362 538 0.205 1.46 164.36 0.75

EngineBottomPlate 40 524 162 2 20 10 460 357 0.309 10.00 762.94 0.55

EngineFrontCover 41 264 77 9 9 5 207 225 0.293 1.73 176.55 0.66

EngineGudgeonPin 42 40 4 5 1 1 25 8 0.091 3.57 265.98 0.52

Ferrule2InchClampTubeO

DwSealGroovePt1 43 208 19 6 6 6 158 152 0.089 1.12 170.49 0.88

Ferrule2InchClampTubeO

DwSealGroovePt2 44 101 45 2 6 6 94 57 0.451 3.01 250.53 0.21

fitting 45 33 4 5 2 2 24 8 0.108 2.71 203.28 0.56

Flange 46 322 73 8 13 12 378 510 0.227 1.68 207.52 0.86

FlyWheel 47 348 92 9 4 9 218 228 0.265 2.34 200.38 0.60

FordGT40IntakeSpacer 48 410 95 34 1 9 638 267 0.232 35.31 3636.82 0.64

FuelPumpDeletePlate 49 61 12 6 5 1 56 14 0.201 10.00 853.14 0.15

gasket 50 2795 390 80 25 0 4036 596 0.140 266.67 184956.67 0.35
62 

Gear 51 563 244 14 14 2 416 325 0.433 7.20 679.26 0.25

GearboxCasing 52 6386 3046 66 45 8 5254 14064 0.477 8.72 733.23 0.78

GearBoxTophousing 53 5946 6377 48 28 12 4105 14760 1.072 4.00 317.42 0.57

GenevaCam 54 317 107 14 15 1 367 161 0.338 14.54 1911.01 0.33

GM3RUJoint 55 154 94 9 9 3 187 170 0.611 3.22 227.41 0.45

GMLS6FrtCover 56 1708 401 32 27 5 1527 2184 0.235 6.18 745.99 0.82

HelicalGearWheel 57 779 225 14 14 4 483 615 0.289 3.50 298.25 0.63

HondaNSR125Cylinder

HeadGasket 58 93 1 10 10 0 153 2 0.012 328.54 659909.64 0.53

Housing 59 644 209 11 11 8 390 601 0.325 1.34 164.57 0.65

HousingSquare 60 971 575 15 14 6 702 1144 0.592 2.47 264.25 0.50

IgnitionCoilMazda13B 61 194 73 4 9 9 164 142 0.375 2.60 221.13 0.49

Impeller 62 288 63 8 6 8 175 208 0.218 1.33 123.36 0.70

IntakeMobilPart1 63 1819 1014 33 9 8 1230 2270 0.557 4.41 361.16 0.55

IntakePipeComponent-1 64 176 32 6 5 8 142 122 0.183 1.59 194.76 0.74

IntakeTrumpet 65 82 3 4 4 4 64 42 0.032 1.06 153.80 0.94

JettaActuatorBracket 66 106 15 8 6 5 122 78 0.137 1.52 297.09 0.81

link 67 727 402 40 13 2 835 670 0.553 20.21 1298.01 0.40

LockNuts 68 12 1 2 2 1 9 2 0.063 1.75 168.47 0.64

LowerThermostatHousing

SpacerGM 69 103 24 12 3 1 110 39 0.233 12.83 876.92 0.38

M20LiftingEyeBolt 70 167 58 7 12 3 157 117 0.349 4.03 282.70 0.50

ManifoldPlate 71 430 149 33 7 1 507 250 0.347 27.54 2081.82 0.40

MasterCylinderBracket 72 559 88 13 9 13 627 1037 0.157 1.48 229.36 0.92

Miata16IntakeFlange 73 483 137 34 9 1 629 264 0.284 36.22 3586.81 0.48

MitsubishiEVOMAPadapter 74 58 13 6 2 3 47 24 0.233 2.52 191.90 0.43

NeedleValveScrew 75 5 0 1 3 1 5 1 0.064 4.70 309.13 0.47

OerlikonBrakeValve 76 1606 812 18 6 24 1126 2008 0.505 4.29 354.10 0.60

OilCoolerBypasCover

PlateForVW 77 217 111 9 6 3 184 144 0.512 3.50 300.79 0.23

OilFilter 78 1533 2768 12 15 12 710 1535 1.806 1.26 152.17-0.801 

OilPan 79 4452 1217 51 8 24 3097 6854 0.273 6.43 632.10 0.82
63 

OilPanModel2 80 1546 123 19 3 34 1259 1043 0.080 13.45 1835.42 0.88

OldhamCoupling 81 775 850 15 8 15 638 1221 1.097 1.96 174.25 0.30

ParametricFlange 82 23526 42614 135 68 43 19839 167630 1.811 3.18 277.87 0.75

piston 83 655 420 11 11 11 480 850 0.642 1.05 153.62 0.51

PistonRodPart1 84 196 57 6 17 2 221 121 0.294 11.50 741.03 0.52

PistonRodPart2 85 145 47 11 6 3 165 130 0.322 3.67 264.93 0.64

pitch2 86 108 40 6 6 2 86 46 0.371 3.82 304.58 0.13

PlenumPlate 87 1409 418 40 1 18 1466 444 0.297 63.19 16026.04 0.06

Porsche968Flange 88 202 52 17 8 1 291 118 0.257 18.35 1769.83 0.56

Porsche968IntakeFlange 89 573 186 46 2 7 715 447 0.325 28.94 1832.44 0.58

PorscheStrutBarTopBrace 90 87 18 11 1 5 89 19 0.207 21.79 1966.39 0.05

PressurePlate 91 176 41 8 2 8 126 80 0.236 4.00 310.38 0.48

PulleyForAlternator 92 286 63 6 7 7 161 174 0.221 1.17 137.78 0.64

RockerArm 93 758 695 4 36 7 801 951 0.916 9.00 568.10 0.27

SkidPlateBracket 94 495 71 16 19 12 649 918 0.144 1.52 324.72 0.92

socket 95 280 153 14 8 4 232 234 0.549 3.38 226.56 0.35

SpiralBevelGear 96 269 175 11 3 11 245 217 0.652 3.67 313.46 0.19

SplitPin 97 2 0 0 3 1 3 0 0.031 25.08 1225.96 0.49

sproket 98 0 0 0 0 0 0 0 0.008 8.54 862.56 0.42

SpurGear 99 449 154 15 15 2 411 256 0.343 9.82 1058.35 0.40

SteeringKnuckleFlangeSpacer 100 155 98 14 14 1 294 85 0.631 22.07 3541.99 -0.151 

StraightScrewJoint 101 28 4 3 2 2 21 8 0.154 1.58 158.40 0.42

T3DividedTurboInletFlange 102 181 56 11 1 7 185 90 0.311 8.50 771.25 0.38

ThreeTubeJoint 103 137 51 14 12 2 258 203 0.375 5.65 418.39 0.75

ThrustBearingDisc 104 71 11 6 5 1 69 16 0.160 11.82 1290.09 0.28

TowbarElectricsBracket 105 311 29 8 30 4 440 282 0.094 8.27 1070.98 0.90

TrussBearing 106 817 495 21 7 9 634 1025 0.606 3.05 242.18 0.52

TurboHousing 107 4828 1970 37 16 34 2806 10953 0.408 2.28 184.07 0.82

valve 108 35 7 4 4 10 78 41 0.191 2.91 281.38 0.84

ValveClip 109 2 0 1 1 0 2 0 0.044 2.00 238.07 0.47
64 

VWGolfInletFlange 110 207 40 11 7 3 202 158 0.192 4.52 331.82 0.75

W05Lockwasher 111 17 1 4 4 0 29 4 0.040 13.40 1809.52 0.82

WheelBearingHousingForAVW 112 237 61 9 9 3 208 175 0.259 3.41 292.83 0.65

WINCHMTGBRK 113 1644 484 25 15 21 1875 5308 0.294 1.63 234.10 0.91

WormGear 114 437 271 6 6 28 405 484 0.620 4.67 284.50 0.44

WormGearDesign 115 2075 3160 28 28 10 1718 4758 1.523 2.80 224.13 0.34

WristPin 116 84 13 2 2 6 56 28 0.151 2.70 225.81 0.54

1

The density value should be a positive a value as the volume of the convex hull of an object cannot be less than the volume of the object. It appears that some of the normals for these meshes were not 

pointed in the correct direction. These negative values were omitted in the analysis.

Table B1. Calculated Metrics (continued)

FileName

Smoothness: 

Hull 

Crumpliness

Surface 

Area/

CHarea

Smoothness: 

Crinkliness

Ratio of surface area 

to surface area of 

sphere with same 

volume as object

Cap Ridge Flat Saddle Rut Cup

Normalized

Length of

Sharp Edges

DX/DY DX/DZ DY/DZ

1inchCarbSpacer 0.94 2.60 0.012 0.125 0.598 0.059 0.199 0.007 13.02 5.91 0.93 0.16

4cylinderEngineHeadGasket 0.49 10.58 0.019 0.174 0.697 0.110 0.000 0.000 8.58 269.86 2.37 0.01

944BellhousingBase 0.63 3.06 0.008 0.172 0.624 0.056 0.139 0.000 5.99 19.25 1.07 0.06

944to911OuterCVAdapter 1.24 3.16 0.017 0.367 0.129 0.062 0.407 0.018 13.40 0.35 0.35 1.00

9BladeImpeller 1.49 2.60 0.022 0.272 0.370 0.050 0.284 0.001 11.89 1.87 1.00 0.54

9InchPinSupport 1.32 2.40 0.027 0.367 0.275 0.080 0.233 0.016 16.51 2.27 1.00 0.44

AlumPIPE 1.40 6.98 0.111 0.358 0.016 0.103 0.331 0.082 3.76 2.51 1.54 0.61

Audi20VExhaustFlange 0.70 4.23 0.104 0.180 0.351 0.322 0.040 0.004 9.57 4.89 53.75 11.00

AudiBearingRetainerTool 1.15 2.11 0.018 0.281 0.543 0.012 0.144 0.002 3.74 1.37 1.00 0.73

AudiVWRearCrankPlate 0.77 3.84 0.030 0.224 0.495 0.110 0.128 0.013 12.52 9.56 1.18 0.12

BaseBracket 1.05 2.01 0.011 0.114 0.772 0.018 0.085 0.000 5.26 1.51 2.13 1.41
65 

BearingBody 1.16 2.14 0.010 0.287 0.366 0.069 0.266 0.001 7.18 0.89 0.43 0.49

BevelGear 1.18 2.18 0.033 0.487 0.330 0.019 0.124 0.007 12.08 0.25 0.25 1.00

BigBlockChevyFlange 0.63 3.77 0.122 0.231 0.287 0.318 0.043 0.000 7.30 6.34 50.69 8.00

Block 1.53 3.01 0.090 0.369 0.193 0.079 0.256 0.014 13.94 1.50 1.50 1.00

BOVTop2 1.19 2.78 0.040 0.234 0.392 0.071 0.249 0.013 9.83 4.75 1.04 0.22

BRACKET 1.01 4.63 0.003 0.153 0.668 0.030 0.146 0.000 7.98 3.13 0.67 0.21

BRE14LI4NeedleSleeve

BearingBody 1.24 5.68 0.022 0.546 0.130 0.070 0.232 0.001 27.26 1.01 0.38 0.38

BusBar2Cells40152S 0.97 3.64 0.033 0.105 0.825 0.029 0.008 0.000 4.50 40.73 3.10 0.08

CamRetainer 0.62 3.99 0.042 0.154 0.696 0.092 0.016 0.000 5.51 1.41 44.69 31.67

camshaft 0.78 2.50 0.122 0.682 0.058 0.136 0.002 0.000 5.32 0.08 1.00 12.50

CarburatorBody 1.34 4.68 0.055 0.384 0.141 0.072 0.318 0.029 7.34 0.49 0.48 0.99

CastAluminumIntake 1.35 5.07 0.106 0.308 0.128 0.069 0.331 0.058 5.72 1.47 1.52 1.03

CastExhaustCollector 1.47 7.15 0.099 0.352 0.006 0.035 0.502 0.006 5.46 1.41 1.07 0.76

CetrifugalImpeller 1.91 5.02 0.006 0.267 0.209 0.115 0.396 0.007 8.76 2.10 1.00 0.48

ChevyHeaderFlange 1.08 4.21 0.030 0.281 0.264 0.127 0.287 0.011 4.70 4.67 2.10 0.45

ClutchCover 1.19 7.02 0.013 0.238 0.301 0.222 0.202 0.024 17.60 4.00 1.00 0.25

ClutchPlate1 1.44 4.48 0.013 0.421 0.395 0.037 0.125 0.008 12.95 1.00 6.00 6.00

Collar1inShaft 1.16 2.22 0.037 0.312 0.316 0.062 0.268 0.005 11.17 1.00 3.50 3.50

CollarShaft 0.88 2.36 0.001 0.173 0.581 0.016 0.227 0.000 6.84 6.00 1.00 0.17

ConnectingRod 1.08 2.71 0.045 0.322 0.357 0.062 0.204 0.011 6.17 6.07 3.64 0.60

CoverPlate 1.11 8.51 0.012 0.136 0.799 0.011 0.042 0.000 6.84 2.36 1.33 0.56

CrankGear 1.05 5.52 0.067 0.364 0.154 0.133 0.261 0.022 26.32 10.66 1.00 0.09

Crankshaft 0.90 3.46 0.147 0.329 0.344 0.118 0.062 0.000 11.61 0.53 0.13 0.24

CylinderBlock5cyl 2.36 7.22 0.013 0.156 0.165 0.093 0.573 0.000 12.10 3.09 4.12 1.33

Diffuser 1.36 3.87 0.033 0.271 0.405 0.071 0.193 0.027 21.33 0.30 0.30 1.00

DISCPLATE 0.88 4.15 0.008 0.093 0.735 0.085 0.079 0.000 9.63 28.33 1.00 0.04

ElbowCastIron 1.34 3.35 0.080 0.236 0.413 0.080 0.153 0.039 8.08 0.87 0.86 0.98

EngineBlock 1.78 5.14 0.033 0.317 0.215 0.057 0.364 0.013 12.21 0.72 0.68 0.95

EngineBottomPlate 1.14 3.64 0.014 0.230 0.574 0.034 0.145 0.004 15.18 0.10 0.20 2.00
66 

EngineFrontCover 1.28 3.01 0.017 0.321 0.331 0.039 0.286 0.006 12.63 1.00 1.73 1.73

EngineGudgeonPin 1.61 3.52 0.015 0.519 0.022 0.050 0.394 0.000 4.84 3.57 3.57 1.00

Ferrule2InchClampTubeO

DwSealGroovePt1 1.32 6.14 0.016 0.465 0.077 0.030 0.409 0.004 8.86 0.89 0.89 1.00

Ferrule2InchClampTubeO

DwSealGroovePt2 1.08 1.64 0.024 0.374 0.515 0.029 0.056 0.001 6.23 0.33 0.33 1.00

fitting 1.40 2.93 0.051 0.432 0.132 0.040 0.345 0.000 5.42 2.71 2.35 0.87

Flange 0.85 3.81 0.001 0.075 0.722 0.024 0.171 0.007 8.66 0.60 0.67 1.13

FlyWheel 1.59 3.53 0.038 0.346 0.246 0.056 0.276 0.039 18.84 2.34 1.00 0.43

FordGT40IntakeSpacer 0.64 4.07 0.127 0.147 0.222 0.355 0.145 0.003 10.13 35.31 3.66 0.10

FuelPumpDeletePlate 1.09 2.37 0.017 0.134 0.633 0.026 0.160 0.030 4.99 1.19 10.00 8.43

gasket 0.69 10.83 0.009 0.111 0.755 0.125 0.000 0.000 12.37 3.20 266.67 83.33

Gear 1.35 2.98 0.057 0.280 0.402 0.082 0.176 0.004 33.64 1.00 7.20 7.20

GearboxCasing 1.22 6.28 0.057 0.172 0.485 0.099 0.158 0.029 8.39 1.46 8.72 5.97

GearBoxTophousing 1.45 3.58 0.032 0.107 0.587 0.054 0.201 0.018 15.82 1.71 4.00 2.33

GenevaCam 0.86 2.90 0.009 0.111 0.706 0.052 0.121 0.000 7.92 0.95 13.88 14.54

GM3RUJoint 0.82 1.54 0.056 0.663 0.136 0.132 0.013 0.000 1.56 1.00 3.22 3.22

GMLS6FrtCover 1.12 6.50 0.054 0.184 0.497 0.083 0.163 0.019 7.45 1.20 6.18 5.14

HelicalGearWheel 1.61 4.35 0.019 0.210 0.421 0.046 0.299 0.005 34.08 1.00 3.50 3.50

HondaNSR125Cylinder

HeadGasket 0.61 18.16 0.007 0.301 0.451 0.049 0.191 0.001 7.92 1.07 328.54 306.94

Housing 1.65 3.78 0.022 0.272 0.202 0.111 0.354 0.039 18.09 1.00 1.34 1.34

HousingSquare 1.38 2.91 0.003 0.063 0.487 0.052 0.382 0.013 13.20 1.09 2.47 2.27

IgnitionCoilMazda13B 1.18 2.30 0.029 0.405 0.363 0.039 0.154 0.010 8.08 0.39 0.38 0.98

Impeller 1.65 3.77 0.009 0.283 0.407 0.104 0.197 0.000 11.36 1.33 1.00 0.75

IntakeMobilPart1 1.48 3.73 0.001 0.253 0.582 0.050 0.108 0.007 11.55 3.54 4.41 1.25

IntakePipeComponent-1 1.24 3.60 0.022 0.427 0.104 0.073 0.368 0.007 5.56 1.14 0.72 0.63

IntakeTrumpet 1.27 8.99 0.081 0.335 0.057 0.140 0.323 0.063 0.41 1.00 0.94 0.94

JettaActuatorBracket 0.87 3.69 0.003 0.091 0.832 0.031 0.042 0.001 6.48 1.36 1.52 1.12

link 0.87 2.76 0.029 0.196 0.606 0.051 0.118 0.000 1.70 3.14 20.21 6.43

LockNuts 1.33 3.00 0.053 0.235 0.221 0.046 0.227 0.218 9.72 1.00 1.75 1.75

LowerThermostatHousing

SpacerGM 0.94 2.56 0.019 0.199 0.664 0.035 0.083 0.000 6.64 3.59 12.83 3.57
67 

M20LiftingEyeBolt 1.06 2.30 0.377 0.150 0.031 0.433 0.007 0.003 36.22 0.59 2.39 4.03

ManifoldPlate 0.85 3.16 0.026 0.178 0.534 0.133 0.122 0.007 7.39 4.95 27.54 5.56

MasterCylinderBracket 0.89 5.85 0.004 0.099 0.837 0.030 0.029 0.001 7.48 1.46 0.99 0.68

Miata16IntakeFlange 0.77 3.75 0.041 0.196 0.469 0.190 0.103 0.000 9.27 3.98 36.22 9.09

MitsubishiEVOMAPadapter 1.21 2.11 0.075 0.232 0.435 0.075 0.176 0.007 8.05 2.52 2.45 0.97

NeedleValveScrew 1.01 2.16 0.302 0.401 0.106 0.172 0.018 0.000 13.51 0.21 1.00 4.70

OerlikonBrakeValve 1.43 3.82 0.021 0.227 0.534 0.041 0.165 0.011 18.49 3.21 0.75 0.23

OilCoolerBypasCover

PlateForVW 1.18 1.94 0.010 0.137 0.609 0.048 0.175 0.022 8.50 1.44 3.50 2.42

OilFilter 2.16 1.61 0.060 0.592 0.227 0.052 0.055 0.014 11.58 0.79 1.00 1.26

OilPan 1.44 8.07 0.014 0.159 0.568 0.074 0.165 0.021 12.66 6.43 2.14 0.33

OilPanModel2 1.23 12.92 0.038 0.232 0.507 0.039 0.160 0.024 3.62 7.35 0.55 0.07

OldhamCoupling 1.22 1.79 0.004 0.375 0.435 0.023 0.163 0.000 5.61 1.96 1.00 0.51

ParametricFlange 1.19 3.99 0.003 0.271 0.454 0.050 0.219 0.004 15.48 1.99 3.18 1.60

piston 1.36 2.41 0.016 0.500 0.228 0.032 0.219 0.004 17.14 1.00 0.95 0.95

PistonRodPart1 0.88 2.72 0.027 0.170 0.382 0.090 0.311 0.020 7.65 0.35 4.00 11.50

PistonRodPart2 0.88 2.31 0.041 0.320 0.328 0.034 0.265 0.012 6.39 1.97 3.67 1.86

pitch2 1.25 1.91 0.016 0.241 0.476 0.144 0.095 0.027 10.85 1.00 3.82 3.82

PlenumPlate 0.96 5.21 0.023 0.059 0.866 0.051 0.001 0.000 4.97 63.19 2.20 0.03

Porsche968Flange 0.69 3.00 0.024 0.211 0.468 0.092 0.202 0.004 7.27 2.06 18.35 8.89

Porsche968IntakeFlange 0.80 3.64 0.093 0.198 0.249 0.224 0.236 0.001 7.79 28.94 6.87 0.24

PorscheStrutBarTopBrace 0.97 2.61 0.004 0.112 0.845 0.023 0.015 0.000 3.05 21.79 2.14 0.10

PressurePlate 1.40 3.03 0.024 0.295 0.364 0.062 0.252 0.003 12.14 4.00 1.00 0.25

PulleyForAlternator 1.78 3.73 0.080 0.287 0.287 0.051 0.286 0.009 7.45 0.85 0.85 1.00

RockerArm 0.95 2.00 0.019 0.162 0.682 0.027 0.106 0.004 5.58 0.11 0.57 5.14

SkidPlateBracket 0.76 5.96 0.010 0.154 0.753 0.052 0.031 0.001 6.33 0.84 1.28 1.52

socket 1.21 2.02 0.030 0.342 0.369 0.042 0.212 0.005 7.13 1.72 3.38 1.96

SpiralBevelGear 1.10 1.77 0.012 0.403 0.474 0.015 0.095 0.002 11.15 3.67 1.00 0.27

SplitPin 0.79 2.74 0.122 0.795 0.004 0.079 0.000 0.000 0.21 0.04 0.22 5.58

sproket 0.99 2.80 0.043 0.130 0.464 0.122 0.240 0.000 10.23 8.38 0.98 0.12
68 

SpurGear 1.09 3.23 0.008 0.140 0.741 0.024 0.085 0.002 15.40 1.00 9.82 9.82

SteeringKnuckleFlangeSpacer 0.53 1.51 0.006 0.213 0.702 0.031 0.044 0.003 3.25 1.03 22.07 21.33

StraightScrewJoint 1.36 2.20 0.029 0.385 0.282 0.050 0.248 0.006 10.28 1.37 1.58 1.15

T3DividedTurboInletFlange 0.98 2.55 0.009 0.122 0.652 0.044 0.173 0.000 7.77 8.50 1.62 0.19

ThreeTubeJoint 0.53 2.05 0.000 0.000 0.011 0.187 0.792 0.009 0.00 1.15 5.65 4.90

ThrustBearingDisc 1.03 2.90 0.026 0.204 0.541 0.088 0.113 0.027 18.59 1.17 11.82 10.10

TowbarElectricsBracket 0.71 6.79 0.029 0.154 0.744 0.051 0.021 0.000 4.73 0.25 2.07 8.27

TrussBearing 1.29 2.70 0.013 0.203 0.547 0.030 0.205 0.002 8.17 3.05 2.39 0.79

TurboHousing 1.72 6.35 0.171 0.302 0.014 0.130 0.248 0.135 7.33 2.28 1.10 0.48

valve 0.45 2.04 0.097 0.648 0.160 0.095 0.000 0.000 0.30 1.00 0.34 0.34

ValveClip 1.02 1.98 0.010 0.489 0.177 0.103 0.219 0.003 4.87 1.23 2.00 1.62

VWGolfInletFlange 1.02 3.68 0.027 0.230 0.333 0.080 0.324 0.005 5.24 1.74 4.52 2.60

W05Lockwasher 0.57 4.48 0.035 0.207 0.669 0.030 0.057 0.001 8.02 1.00 13.40 13.35

WheelBearingHousingForAVW 1.14 3.15 0.020 0.222 0.379 0.090 0.271 0.018 14.21 1.08 3.41 3.15

WINCHMTGBRK 0.88 5.52 0.006 0.147 0.769 0.020 0.057 0.000 6.37 1.63 1.18 0.73

WormGear 1.08 2.16 0.130 0.545 0.201 0.090 0.033 0.001 9.00 1.00 0.21 0.21

WormGearDesign 1.21 1.99 0.025 0.184 0.469 0.152 0.170 0.000 15.55 1.00 2.80 2.79

WristPin 1.51 3.20 0.007 0.565 0.007 0.017 0.405 0.001 2.73 1.00 0.37 0.37
69 

Appendix C: Extended List of Metrics

Table C1. Potential List of Metrics to Characterize an Object

Feature/

Descriptor

Local or 

Global

2D / 3D 

/ Both

Shape/Su

rface Description

Relevant (R)

Non-Relevant 

(NR)

Algorithm/

software 

needed 

(Y/N), 

available?

Source

Spin images Local 3D Shape Histogram of local point locations given offset from center, 

oriented point. R Y, available Johnson and Hebert 

1999

Intrinsic Spin Image 

(ISIs) Local 3D Shape A generalization of spin images to use arbitrary subspaces 

rather than basic x,y, rectangular coordinate system NR 

SURF Local 2D Surface 

(texture)

Speeded Up Robust Features (SURF). Local image feature 

detector and descriptor based on Haar wavelet response. 

Scale/rotation invariant.

R Y, available Bay et al., 2006

Color histograms Local/

Global 2D Surface Histogram of color values in appropriate color space 

(RGB, HSB) R Zivkovic and Krose, 

2004

HOG (PHOG) Local 2D Surface

Histogram of Oriented Gradients (HOG). Local image 

feature descriptor. A histogram of local gradient 

orientations computed on subcells in a region, and 

normalized by intensity over a larger block.

R Y, available Dalal and Triggs, 

2005

Self-similarity Local 2D Surface Log-polar histogram descriptor of local point features. R Shechtman and Irani, 

2007

SIFT Local 2D Surface

Scale Invariant Feature Transform (SIFT). Local feature 

vector computed from histogram of local gradients and 

intensities.

R Y, available Lowe, 2004

2.5D SIFT Local Shape + 

surface Generalization of SIFT to 2.5D range images. R Lo and Siebert, 2009
70 

Feature/

Descriptor

Local or 

Global

2D / 3D 

/ Both

Shape/Su

rface Description

Relevant (R)

Non-Relevant 

(NR)

Algorithm/

software 

needed 

(Y/N), 

available?

Source

Shape context Local Both 

Shape + 

surface 

(pattern)

Shape context. 2D and 3D point feature computed as logpolar histogram of points, typically along boundaries. Can 

be generalized to 3D.

R Y, available Malik et al., 2001

LESH Local 2D Surface

Local Energy Based Shape Histogram (LESH). Local 

image feature descriptor based on 128-dinensional 

compact spatial histogram. Scale invariant.

NR Sarfraz and 

Hellwich, 2008

MSER Local 2D Surface

Maximally Stable Extremal Regions (MSER), A local 2D 

image detector and descriptor that uses image morphology 

to find blob patterns.

NR Y, available Matas et al, 2002

GLOH Local 2D Surface

Gradient Location and Orientation Histogram (GLOH). 

Enhancement of the SIFT operator to use more spatial 

regions.

NR Mikolajczyk and 

Schmid, 2005

Autocorrelation Local 2D Surface

Standard technique for correlating images – power 

spectrum will indicate whether image region is distinctive 

and suitable for matching.

NR Deng et. al, 2007

PCBR Local 2D Surface

Principal Curvature-Based Region (PCBR) region detector. 

A structure based, affine invariant detector that finds 

curvature maximums in scale space.

NR Deng et. al, 2007

Corner detectors Local 2D Surface

Many versions (described in review article Mikolajczyk et 

al.) All are local image feature detectors that are sensitive 

to high curvature, high gradients, and other distinctive 

image extrema.

R Y, available Mikolajczyk et al 

2005

ART (ang. Radial) Global 2D Surface

Angular Radial Transform (ART). Feature descriptor based 

on angular decomposition of B&W image to set of radially 

symmetrical basis functions.

NR Bober, 2001

RIFT Local 2D Surface Rotation-Invariant Feature Transform (RIFT). Rotational 

invariant version of SIFT detector. NR Lazebnik et al, 2005
71 

Feature/

Descriptor

Local or 

Global

2D / 3D 

/ Both

Shape/Su

rface Description

Relevant (R)

Non-Relevant 

(NR)

Algorithm/

software 

needed 

(Y/N), 

available?

Source

Shock Scaffold Global 3D Shape

The shock scaffold is a hierarchical organization of the 

medial axis in 3D consisting of special medial points, and 

curves connecting these points, thereby forming a 

geometric directed graph

R Laymarie and Kimia, 

2001

3D Zernike 

Descriptors Global 3D Shape

A vector of 3D shape descriptors based on affine invariant 

moments of 3D point cloud based on Zernike polynomials, 

which are orthogonal on the unit sphere. 

R Y, available Novotni and Klein, 

2003

Radius-based 

Surface Descriptor 

(RSD) 

Global 3D Shape

Symmetric model fitting from point cloud data, using 

sample consensus to fit generalized cylinders (the 

approximate radius of the smallest fitting curve to a local 

neighborhood.)

R Yes, in 

ROS/PCL Marton et al, 2010

PC (Principal 

Curvature) Local 3D Shape

Local shape descriptor of principle curvature of local 

points. Very general descriptor, generally not useful by 

itself.

R Rusu and Cousins, 

2011

FPFH (Fast Pt. Ft. 

Hist.) Local 3D Shape

6D pose invariant local shape descriptor that generalizes 

mean curvature by encoding neighborhood properties in 

histogram of local normal differential features.

NR Rusu, Blodow, 

Beetz, 2009

Global FPFH Global 3D Shape

A global shape descriptor that uses the FPFH 

classification of local nodes in the creation of pairwise 

histograms between feature points. A ray between each 

pair of ft. pts. is intersected with nodes and a histogram 

generated for that pair of the classes of intersecting nodes.

NR

Rusu, Hozbach, 

Beetz, Bradski, 

2009

3D Shape Context Local 3D Shape

A local shape descriptor computed by a spherically 

indexed histogram of local point position around a given 

point, the north pole given by the surface normal at the 

given point. 

R Tombari et al, 2010

VFH (Viewpt. Ft. 

Hist.) Local 3D Shape A local shape descriptor based on the FPFH that integrates 

the viewpoint normal into the histogram calculations. R Rusu, Bradski, 

Thibaux, Hsu, 2010

Point Signature Local 3D Shape

Point descriptor [Chua and Jarvis [CJ97]] used a similar 

sampling, but recorded the distance from the contour to a 

plane fit to the contour and passing through the point.

R Chua and Jarvis, 

1997 
72 

Feature/

Descriptor

Local or 

Global

2D / 3D 

/ Both

Shape/Su

rface Description

Relevant (R)

Non-Relevant 

(NR)

Algorithm/

software 

needed 

(Y/N), 

available?

Source

Intrinsic Shape 

Signatures Local 3D Shape

Local 3D measure based on local support compute the 

Eigen Value Decomposition (EVD) of the scatter matrix of 

the points belonging to the support. ISS uses as 

distinctiveness the magnitude of the smallest eigenvalue 

and the ratio between two successive eigenvalues.

R Zhong, 2009

Heat Kernel 

Signatures Local 3D Shape

Local measure based on eigenvalue decomposition of heat 

kernel. Invariant to isometric transformation. Represents 

decomposition into eigenvalues and eigenfunctions of 

Laplace-Beltrami operator.

R Y, available Bronstein and 

Kokkinos, 2010

GPS Global 3D Shape

A deformation invariant representation of surfaces, the 

GPS embedding, is introduced using the eigenvalues and 

eigenfunctions of the Laplace-Beltrami differential 

operator. It is based on objects of global character, the 

obtained representation is robust to local topology changes. 

The GPS embedding captures enough information to 

handle various shape processing tasks as shape 

classification, segmentation, and correspondence.

R Rustamov, 2007

CVFH (Clustered 

ViewPt. Ft. Hist.

Semiglobal 3D Shape

Local 3D shape descriptor of stable regions using a local 

reference frame, building a histogram of angles to other 

points, including Shape Distribution Component (SDC). 

R Aldoma et al, 2012

NARF Local 3D Shape

Normal Aligned Radial Feature is a local 3D shape 

detector and descriptor for point cloud data, a histogram of 

curvature changes along radial directors. 

R Steder et al., 2010

HK Segmentation Local 3D Shape Gaussian (K) and mean (H) curvature measures computed 

for each local point. R Y, available Besl and Jain, 1986

SC Shape Index Local 3D Shape

A revised version of H and K that decouples the shape 

characteristic (nature of curvature) and shape strength 

(magnitude of curvature.)

R Y, available Koenderink and van 

Doorn, 1992

Degree of 

symmetry/Bilateral 

or radial symmetry

Global Both Shape Some number which shows how symmetric an object is. NR 
73 

Feature/

Descriptor

Local or 

Global

2D / 3D 

/ Both

Shape/Su

rface Description

Relevant (R)

Non-Relevant 

(NR)

Algorithm/

software 

needed 

(Y/N), 

available?

Source

Chirality Global Both Shape

Chirality is a property of asymmetry important in several 

branches of science. 

An object or a system is chiral if it is not identical to its 

mirror image, that is, it cannot be superposed onto it.

NR

Compactness Global Both Shape

The compactness measure of a shape, sometimes called 

the shape factor, is a numerical quantity representing the 

degree to which a shape is compact

The compactness measure of a shape, sometimes called the 

shape factor, is a numerical quantity representing the 

degree to which a shape is compact

R Y, available MacEachren, 1985

Convexity Global Both Shape

Definition 1. For a given 3D closed mesh M, where the 

convex hull of M is CH(M), we define its convexity 

measure C1(M) as

C1(M) = Volume(M) / Volume(CH(M))

Definition 2. For a given 3D closed mesh M, where the 

convex hull of M is CH(M), we define its convexity 

measure C2(M) as

C2(M) = SurfaceArea(M) / SurfaceArea(CH(M))

R Y, available

Žunić, J. and Rosin, 

P. L. , 2004

Ellipticity Global Both Shape How elliptical is the 3D model? NR Aktaş and Žunić, 

2011

Rectangularity Global Both Shape How rectangular is the 3D model? NR Rosin, 2003

Rectilinearity Global Both Shape How rectilinear is the 3D model? NR Žunić, J. and Rosin, 

P. L., 2003

Triangularity Global Both Shape How triangular is the 3D model NR Rosin, 2003

Roundness Global 3D Shape

Roundness is the degree of smoothing due to abrasion of 

sedimentary particles. It is expressed as the ratio of the 

average radius of curvature of the edges or corners to the 

radius of curvature of the maximum inscribed sphere.

R Y, available

Wadell, 1932
74 

Feature/

Descriptor

Local or 

Global

2D / 3D 

/ Both

Shape/Su

rface Description

Relevant (R)

Non-Relevant 

(NR)

Algorithm/

software 

needed 

(Y/N), 

available?

Source

Sphericity Global 3D Shape

Sphericity is a measure of how spherical (round) an object 

is. As such, it is a specific example of a compactness 

measure of a shape. 

NR Y, available

Mora and Kwan, 

2000

Volume Global 3D Shape Volume of model R Y, available Corney et al., 2002

Surface area Global 3D Shape Surface area of model R Y, available Corney et al., 2002

Volume/Surface 

Area Global 3D Shape Volume/Surface Area of model R Y, available Corney et al., 2002

Bounding box 

aspect ratio Global 3D Shape Ratio of the longest edge to the shortest edge. R Y, available Corney et al., 2002

Crinkliness Global 3D Shape

Defined as the surface area of the model divided by the 

surface area of a sphere having the same volume as the 

model.

NR Jayanti et al., 2006

Hull compactness Global 3D Shape Non-dimensional ratio of convex hull’s surface area cubed 

to volume of convex hull squared NR Corney et al., 2002

Number of facets Global 3D Shape Number of facets on the model NR Corney et al., 2002

Number of holes Global 3D Shape No of holes in a 3D model R Corney et al., 2002

Hull crumpliness Global 3D Shape Ratio of object surface area to surface area of its convex 

hull NR Corney et al., 2002

Hull packing Global 3D Shape

% of convex hull volume not occupied by original object 

and is equal to:

1 − Vmodel

Vhull

NR Corney et al., 2002

D1 Global 3D Shape Histogram of radius R Y, available

Osada, R., 

Funkhouser, T., 

Chazelle, B. and 

Dobkin, D
75 

Feature/

Descriptor

Local or 

Global

2D / 3D 

/ Both

Shape/Su

rface Description

Relevant (R)

Non-Relevant 

(NR)

Algorithm/

software 

needed 

(Y/N), 

available?

Source

D2 Shape 

distribution Global 3D Shape A histogram of distances between pairs of points on the 

surface R Y, available Osada, 2001 (in 

Shilane et al., 2006)

Moments Global 3D Shape Moment (Hu, Zernike, etc) of models R Y, available Novotni and Klein, 

2003

Extended Gaussian 

images (EGI) Global 3D Shape Spherical function giving the distribution of surface normals R Horn, 1984 (in Shilane et al., 2006)

Shape histograms - 

SHELLS Global 3D Shape Histogram of distances from the center of mass to points 

on the surface R 

Ankerst et al., 1999 

(in Shilane et al., 

2006)

Shape historgrams - 

SECTORS Global 3D Shape A spherical function giving the distribution of model area 

as a function of spherical angle R 

Ankerst et al., 1999 

(in Shilane et al., 

2006)

Spherical harmonic 

descriptor (SHD) Global 3D Shape

A rotation invariant representation of the GEDT obtained 

by computing the restriction of the function to concentric 

spheres and storing the norm of each (harmonic) frequency

R Y, available

Kazhdan et al. 2003 

(in Shilane et al., 

2006)

Spherical extent 

function (EXT) Global 3D Shape

A spherical function giving the maximal distance from 

center of mass

as a function of spherical angle

R 

Saupe and Vranic, 

2001 (in Shilane et 

al., 2006)

Radialized spherical 

extent function 

(REXT)

Global 3D Shape

A collection of spherical functions giving the maximal 

distance from center of mass as a function of spherical 

angle and radius

R Vranic 2003 (in 

Shilane et al., 2006)

3D Wavelet 

descriptor Global 3D Shape

They propose the usage of spherical wavelet transform as 

a tool for the analysis of 3D shapes represented by 

functions on the unit sphere. We introduce three new shape 

descriptors extracted from the spherical wavelet 

coefficients, namely: (1) a subset of the spherical wavelet 

coefficients, (2) the L1 and, (3) the L2 energies of the 

spherical wavelet sub-bands.

R Laga H. et al., 2006

Skeleton descriptor Global 3D Shape Skeleton descriptor R Li, Chunyuan, 2013

Reeb graph 

descriptor Global 3D Shape Skeleton descriptor R Li, Chunyuan, 2013
76 

Feature/

Descriptor

Local or 

Global

2D / 3D 

/ Both

Shape/Su

rface Description

Relevant (R)

Non-Relevant 

(NR)

Algorithm/

software 

needed 

(Y/N), 

available?

Source

Light field 

descriptor (LFD) – 

View base

Global 3D Shape

A representation of a model as a collection of images 

rendered from uniformly sampled positions on a view 

sphere. The distance between two descriptors is defined as 

the minimum L1-difference, taken over all rotations and 

all pairings of vertices on two dodecahedra.

R Y, available

Chen et al., 2003 (in 

Shilane et al., 2006)

[10]

DESIRE Global 3D Shape

Composite 3D-shape feature vector (DESIRE), which is 

formed using depth buffer images, silhouettes, and rayextents of a polygonal mesh. R Y, available Vranic, D. V

View based with 2D 

Polar-Fourier 

coefficients, Zernike 

moments and 

Krawtchouk 

moments, 2D 

Discrete Wavelet 

coefficients

Global 3D Shape

View based method, based on Polar-Fourier coefficients, 

Zernike moments and Krawtchouk moments, 2D Discrete 

Wavelet coefficients

R 

Daras and 

Axenopoulos (2009)

and

Papadakis,, et al., 

2010

Convex Hull 

Histogram (CHH) Global 3D Shape

Compute the 3D convex hull for a given model using the 

Quickhull [Barber et al., 1996] algorithm. Then build a 

histogram of the pairwise distances based on the points 

obtained from the convex hull [Boutin and Kemper, 2004, 

Kalyanaraman et al. 2005]. This method is identical to the 

basic idea described in [Rea et al, 2005] which presents a 

detailed study analyzing the merits of this method.

R Jayanti et al., 2006

3D shape 

histogram—Solid 

Angle Histogram 

Global 3D Shape A histogram based on the Solid Angle between random 

points R 

Ankerst, M., et al. 

1999

Similarity metrics ( 

L1, L2, etc), Bag of 

words approach, 

Sparse coding, 

classifier, etc 

 Both Both General purpose tools R Y, available Ohbuchi, et. al., 

2008

Harmonic shape 

context Local 3D Shape

Harmonic shape contexts (HSC) local features are 

invariant to translation, scale, and 3D rotation. R Y, available Frome, et al., 2007
77 

Feature/

Descriptor

Local or 

Global

2D / 3D 

/ Both

Shape/Su

rface Description

Relevant (R)

Non-Relevant 

(NR)

Algorithm/

software 

needed 

(Y/N), 

available?

Source

Blowing bubbles 

(L1) Local 3D Shape

Blowing bubbles intersects the surface with a set of 

concentric spheres and extracts information about the 

surface in two steps. First, they simply count the number of 

closed contours, ignoring curves that are far away.

NR Y, available Heider, et al., 2011

Geodesic fans (L5) Local 3D Shape

Geodesic fans sample a metric (such as curvature) on the 

mesh using concentric geodesic rings instead of spheres. 

Geodesic fans re-sample the metric into evenly spaced 

samples in the radial and angular direction. 

NR Y, available Heider, et al., 2011

Splash descriptor 

(L2) Local 3D Shape

3D mesh descriptor that computes normal information 

along 3D curves of maximum curvature and converts to 2D 

curve that encodes local curvature and torsion

NR Stein and Medioni, 

1992

Point descriptor (l7) Local 3D Shape

Point descriptor [Chua and Jarvis] used a similar 

sampling, but recorded the distance from the contour to a 

plane fit to the contour and passing through the point

NR Y, available Chua and Jarvis 

Normal Distribution Local 3D Shape It is a local feature based on the normal distribution. R Y, available Heider, et al., 2011

Curvatures: mainly 

four curvature 

values, Mean, 

Gaussian, Shape and 

Curvature index (SI, 

CI) [L2]

Local 3D Shape Based on the Curvatures values the following features are 

calculated: Mean, Gaussian, Shape and Curvature index. R Y, available Heider, et al., 2011

Geodesics, heat and 

diffusion Local 3D Shape

Geodesic and Heat diffusion: The techniques in this class 

do not directly measure the geodesics, but instead measure 

a diffusion process flowing along the geodesics. 

R Y, available Bronstein, 2011
78 

References for Table C1

Aktaş, M. A., and Žunić, J., Measuring shape ellipticity, In Computer Analysis of Images and Patterns, Springer Berlin 

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